Why are there silly license requirements?

Reasons for a license to fish (from a German perspective and with common sense):
You want people who fish to know when they can and cannot fish due to the fish’s [Edit: re pro]creation periods.
You want people to know which kinds of fish they should and should not catch, in general.
You want people to know how big a certain kind of fish needs to be before it can be extracted.
You want a general overview of the number of people fishing in a general area to monitor overfishing.
License to have a dog:
Costs a certain amount of money each month. This funds public cleaning of dog poop and free dog poop bags.
License for a GMRS radio:
To prevent too many people from crowding in the same channel.
To be able to identify assholes who jam a channel with their broadcasts.
License for biking:
To know the rules of the road
- Upvote for thoughtful reply but I think you mean fish procreation periods. Nobody cares what season they go golfing 😆
  
  Thanks for catching that. I’m sure there must be a fish-specific term that’s eluding me.
- This funds public cleaning of dog poop and free dog poop bags.
  NYC technically requires a dog license, and I can guarantee you it provides neither of these things. The streets are absolutely covered in dog shit because of irresponsible dog owners. A lot of the city doesn't have garbage cans either (especially in Queens), and the few that exist are never emptied.
  
  This person knows what's up...
  I don't hate the animal, just the dog owner. These people are inconsiderate parasites that need to be taxed into compliance.
  When did we as society decide that their right to own pets in dense urban setting permits them to spoil any patch of greenery and landscaping?!
- License to have a dog:
  
  Costs a certain amount of money each month. This funds public cleaning of dog poop and free dog poop bags.
  Wait... i never heard of this... where is this utopia located?!
  
  I know of them in Germany. But the duckduckgo image search reveals that they exist in many places.
- How does the dog license get enforced? Do police go around confronting dog walkers?
  
  As with many types of license, they usually only get checked when you're caught misbehaving.
  If you're caught not picking up your dogs poo, you're asked "have you got a licence for that dog". At which point, if you say no, then you get another charge or two slapped on as well. If you lie and say yes you can get yet another charge slapped on for lying to law enforcement.
  Its basically another layer of incentive to follow the law and get a license or the penalties may be higher as a result.
  
  In Germany we have a law enforcement level below the police called “Ordnungsamt” (I’m not going to try to translate that). They are in charge of these minor misdemeanors (like parking wrong, littering, speeding, etc.) It’s entirely possible that their patrols randomly check dog owners, but personally I’ve never heard of that.

License to fish: prevents over fishing
license to bike: for road safety (mopeds and cars in the UK are on the provisional license so that's a none issue)
lisense to use a radio: some frequencies are restricted usage for airports, military, ect, and high powered radios can be used to create interference.
license to exist: Your NeuroLink Subscription Will Expire in Seven Days After Which You Will Cease To Exist and Your Body Will Be Recycled into Nutrients.

When the State licenses things like that, it's usually because whatever activity is being licensed utilizes shared resources, and the State has an interest in making sure those resources are used in the common interest.
Radio licenses are essential because the RF spectrum is a common resource. The State wants to make sure that certain frequencies are only used for certain purposes, and that those who use them have the proper training.
Some communities use pet licensing as a tool to make sure all pets are properly vaccinated, to reduce the spread of rabies (which really is a horrible way to go....)
Hunting and fish licenses are a way to help control the overall wild animal population, and make sure they are not overharvested and preserve rhe availability for future seasons.

Much of license requirements are based on the fact that operating without proper knowledge can cause issues. You mentioned radio, which is a perfect example of this: emergency frequencies is one thing, but there are a lot of other frequencies that should be left alone. And learning which frequency ranges should and shouldn't be used for certain activities is part of the process of obtaining a license.
Source: I have a GOC (unrestricted maritime radio certificate).
Real life example that I stumbled across as part of my job a few years ago.
Customer calls in needing help with his VHF radio.
It worked fine but his DSC calls were often traced to the wrong position.
Turns out some little dinghy had an incorrectly programmed radio: The owner had bought it, and when faced with question about MMSI, he had just input numbers that vaguely resembled a valid MMSI, and started using it.
Oops, this "bogus" MMSI belonged to our customer.
He was fined a lot for operating without a license. If he was licensed (He didn't need the full GOC... just the one day course would've been enough for his use case) he would've known that he could have gotten his own MMSI for 20$ equivalent.
Other licenses are often based on covering costs, reducing popularity, or both. Hunting licenses here are issued based on how much moose and deer is in the area. This also covers the cost of building infrastructure to prevent them from running across roads where they really shouldn't, and repairing farmers' fences that have been "traversed" by moose.
Fishing in the river that runs through my town is also licensed in a similar manner: The amount (and price) of licenses is based on how much salmon there is.

Because people suck and they can’t be trusted to use common sense.
- Yet somehow the same people can be trusted to select the best among them to make the rules for everyone.

People abuse things.
- Small minority of bad faith actors are essentially able to block us from having nice things... makes you wonder...
  
  Small minority of bad faith actors are essentially able to block us from having nice things
  The rich 1%...
  🤔

There are plenty of activities that are perfectly harmless when done by one person, but need to be managed when a bunch of people try to do them at once.

Where do you need a licence to ride a bike?
The fish license is to control fish population and prevent overfishing as well as funding the wildlife and parks departments.

No idea about bike licenses.
High power radios in the hands of people who don't know what they're doing can cause a lot of issues. FRS/GMRS radios under 2 Watts in the U.S. don't need a license. Licensing is a way to make sure people using them know how to do so effectively, and provides for stiffer penalties if someone unlicensed causes issues.

So you understand the rules, regulations, and hazards of doing those activities.

You didn't mention the TV license (UK)

There are 14 GMRS frequencies. How soon do you think they would become unusable if even 10,000 casual users in a metro area all went and bought 50W radios?
Imagine hundreds of thousands of uneducated users, even 5 year old children, who could just “punch numbers in” - this is what the Baofeng debacle opened up.

Don't forget about poetic license. They regulate everything these days.

License to have licenses

I suppose all activities you need a license for are activities where you must have a higher-than-usual level of responsibility. (Except for the TV license, that's a misnomer and should be called a tax or a due)

What country? 🙄

I've got a license to confuse. What've you got to lose?

Why isn’t there a license to have a kid? With an exam to make sure you’re going to look after them properly?
- Because what would happen is:
  "Are you Black, Hispanic, Asian, Native? Welp, license to have children denied."
- While it seems logical at first, when you consider it seriously it quickly falls apart.
  Even not considering such questions as "How do you enforce it?" (What are you going to do? Take the kid from them? That would quickly turn into a giant mess) or "How effective in actuality it is going to be?" (What stopping someone malicious to ace the exam and then abuse their kid without legal repercussions?) much simpler reason is that it would even further hinder the already falling birth rates. And most of the goverments and people don't want that.

The government likes money, that's why every dollar you spend gets taxed 3 times. Secondarily a barrier to entry limits participation and creates greater opportunity to fine and make even more money than the license or permit.