I'm all for biking everywhere, but depending on the state of the roads in your city, you'll want a decent enough bike to handle potholes and the general shakiness you'll get from uneven road. That makes the inexpensive part utter bullshit, especially because bike theft is a huge problem. I've had enough stolen that I now don't cycle anywhere without indoor secure parking.
It's a bike, you just... Don't hit the pot hole. They are small and agile vehicles, it really isn't that hard unless it'd a literal sink hole in which case a car isn't going over it either
Maybe the roads are pretty good where you are, but in the UK you're forced to the side of the road, and there are loads of holes that wear down your bike. They're bad enough that I've had to switch away from my ebike and road bike into using a mountain bike to get around.
Being "agile" is good and all when you're not sharing the road with dozens of 1T killing machines...
I hit one once because it was dark and I didn't see it it time (despite the streetlights and my own light). Literally hit the road head first (thank fuck for helmets)
Plus because my bike is my primary vehicle, I've customised it and kitted it out with everything I need, from rear rack to trailer mounts, I added turn signals and extra safety lights, kevlar lining for my wheels because the shit roads shred my tires.
The bike itself was expensive, but affordable, the additional kit, and the time and labour I put into making it a transport system that perfectly works for me is much harder to replace.
But I'm lucky to live in an area where you can find secure bike cages at transport hubs, and there are enough other bikes around that my clunky 30kg step through frame isn't as desirable as a lightweight carbon fibre roadster frame when someone is going around with the bolt cutters.
My front strobe light has been stolen 8 times though.
That one is baffling. Because I keep my saddle bags on my bike at all times, so you'd think someone would take those, or at least have a rummage through them and take my tool kit or pump or stuff. Or steal any number of the expensive fixtures I have, like the tail light that plugs into my brakes, or the actual bike flood lamp that's attached to the handlebars with a quick release scew.... But no, they keep stealing the $3 headlamp I buy from the dollar store that's cable tied onto the handlebar stem.
I live in a mid-sized city in the UK, and if I lock my bike outside, someone will try to steal it within 30 mins, almost without fail. We've tried getting public bike cages set up, but then motorists get shitty because those portable cages end up taking up space that cars could use.
I've dropped hundreds on bike locks alone, and despite this have had parts of my bike stolen when someone decided that they couldn't get through the lock, or couldn't cut through where I've secured the lock.