I ran my own mail for a couple decades, until it got too time consuming. Now I primarily use Fastmail and I prefer it to Gmail, but still sometimes there are issues of third parties not liking my TLD (rare but happens with certain TLD's), but the biggest issue is when people just assume Gmail even though I've given them and sent them mail from other addresses and done everything I can to have them not send to my Gmail. Some of these are business clients, also. It's not that I haven't mostly moved from Gmail or that I'm not trying, it's that it's difficult. And I may lose some business when it happens.
Yeah, I should note that choice of TLD is important for your primary email. In my experience so far, no one blocks .com/.org/.net. Other TLDs may be trickier.
Yep. Try to stick to 2/3 letter TLDs, some sites check that length is within that range. I have a "fun" tld (in the same vein as myfullna.me) but keep a .net handy that's aliased to it in case it gets rejected.
Indeed, and now that I've been using it for years and many people also use it to contact me, it will be as painful to change it as it would be to drop Gmail.