It's a mid-sized town of about 100k people, but I've really only advertised to a few thousand in one tiny corner of it. Most of my customers live within 10 minutes of me.
I'm a plumber by training, but I'm naturally a bit of a generalist and a life-long tinkerer and have done some work around my own house. I did commercial plumbing for 10 years before I went self-employed. That's the only thing I'm trained at. Nowdays I just watch a lot of YouTube tutorials and sometimes just wing it, too.
Going self-employed was by far the scariest thing I've ever done - lost countless nights worrying about it - but once I jumped, everything just worked out. Probably the best decision I've ever made. Literally today, a customer told me "everything I touch turns to gold." As a plumber, I got a "thank you" maybe twice in 10 years. Now I get genuine gratitude almost daily.
If you'd asked me about going self-employed as a plumber or electrician, I'd have said it's gonna be a battle. But as a handyman, your customer base is way wider thanks to the broad range of services. Plumbing is still a non-negligible part of what I do, but I'd struggle if that was all I offered. Painting is something I do so much that it's one of the few trades I'd actually recommend specializing in.
Go for it - seriously. Even failure isn't as bad as the regret of never trying.