Not my opinion.
It depends on the hobby and how your worldview is.
IMO turning your hobby into your job CAN be a dream come true. Doesn't HAVE to be, but can be.
I think the fact that it is your hobby makes you super passionate about it, you show more effort and enthusiasm, and maybe even a lot of talent. You overlook negative aspects easier and are more satisfied with the activity itself rather than just doing it for the money, which means money will be an ADDITIONAL motivator making you 2 times as motivated (if you earn "enough" for you taste).
Sure it's hard at first, and sure you can not do everything you would want, and sure there is always trouble, either with higher ups or other things.
But is normal work different? Nope.
I show you my comparison (out of my head):
Hobby = Job
+ Motivation
+ Enthusiasm
+ Fun
+ No other job that annoys you
- only a few other hobbies (because of the time the job takes in this particular case of game developer)
- Hard Work
- Meeting the realism of restrictions
- Making your hobby a little less sweet
Hobby + Job
+ Hobby is carefree and unrestricted, creative
+ Hobby is as fun as it can be for you
- You have less time for your hobby, due to your job
- Your hobby is not as focused and you might not be able to get as much done as if it were your job
- You have a job you have to do as well and have to put your energy in. Worst case is you hate your job and it drains a lot of your energy and motivation
- money is the only motivator for your job
For me the positives in option A and the negatives in option B make the decision. The Calculation is easy. If you make your Hobby your Job and you still have at least moderately fun doing it is means you do not only have no job that you hate or find boring, you also can maintain your hobby for a longer time in your daily life and maybe even learn more and more so you might make yourself independent with your own studio one day. You combine hard work (which normally gives a negative feedback) and hobby (which gives a positive feedback) in one creating big motivation for you job, enabling you to do your hobby as your job, enabling a positive feeling while working.
Of course it should be a hobby that you are REALLY passionate about. But if it is, there is nothing speaking against it.
"A means of livelihood" being your hobby is no bad thing, because that it gives you your money does not mean you can't enjoy it anymore. You might have more stress doing it, but then again, you would have that level of stress even in another job (maybe even more) and you can still do creative work which has to do with your hobby in your free time (using the knowledge and experience you gain while working.
Look, you are saying " a hobby is something that should". The way I see it there is no "should" in a hobby. A hobby is what you want it to be and you take it as seriously as you want to. If you are passionate and serious enough about it to make it your job that is your decision and maybe it is the exact RIGHT decision in this case, if you can keep that passion. I know a lot of people who have done it, even if the nature of the hobby obviously varied a lot.