On a financial aspect, self hosting is more expensive most of the time, if you convert time to money, even if you calculate using less than 100$ per hour (In my country we charge about 200$ per work hour)
Should we do that though? I'm choosing between playing PS5 and configuring my home server. I'm not being paid for either of that. But skills I obtain while tinkering with the server actually help me with some tasks at work.
Sure, you can compare to what else you would do in that time slot, but money would be the more general thing (you can compare better, since everything is in the base of money)
Back to your example: time spent on each task is equal -> same value invested but output may have different value (game skills/progress vs IT skills/progress)
So since investing value is the same for both task, you can ignore that part and concentrate on the output.
Depends on how you calculate costs. Like, I have Kodi running on a RPi for home entertainment/theater. There's no way to outsource that, but the RPi is idle most of the time. Adding services to it is effectively or marginally free, except for my time, and there's still a significant time cost to get paid, off-site cloud services set up.
But charging for your own time is kind of disingenuous. You don't include your time in the cost of eating (a Big Mac worth $60??), watching a video, or going on vacation. The only people self-hosting have a personal, hobby/entertainment interest in it, and I think it's more accurate to compare the costs of self hosting with the costs of other forms of entertainment. Do you get more fun-value out of the costs of self hosting or out of a theater ticket?
Well, you can calculate how much money you would make in the time you do hobby, entertainment and eating.
And I bet, "everyone" includes some people, that see setting up home/private IT not as hobby, for those people the comparison is like spending time x or paying amount x (data or/and money) (you could compare it to housekeeping)
In such cases it makes sense to give the spent time a value in data or money, so that it is comparable
Maybe you spend time on selfhosting and now you have less time for other things that need to be done and now you have to outsource it (for money) giving time as well calculateable value