I've not encountered any problems so far, but we do fairly aggressive full stack testing before we deploy OS updates. Linux has gotten a lot more stable across the board, with Fedora being no exception. I wouldn't recommend running it in production it in a way where you couldn't just destroy the VM and rebuild (like a database server).
Version upgrades in the early days weren't great, but recently (last 5 years or so) it's been totally fine.
Prior to that I used to do LTS-style distros, with version upgrades every 2 or 3 years, but I've found that testing the impact of an upgrade is far easier if you're doing incremental changes every 6-12 months.
Also, since CentOS is a well established free alternative to RHEL, the unwritten rules point to CentOS for RedHat based servers.
If you:
1. Need features on the bleeding edge AND
2. Are capable of fixing or working around any problems that come up AND
3. Are willing to do so in terms of time and effort AND
4. Have made a good business case that the benefits are worth the costs and risks
then, sure, go ahead, use Fedora on your servers. Same as anything else: make a carefully considered decision.
You're right, most rpm based companies go with centos or rhel.
Now on desktop, that's a different story. Fedora is pretty much all I use there.
I know CentOS is traditionally for servers, but I've played with installing CentOS7 on a laptop for fun and side project work and it's worked out pretty well for me -- but it's also not my full time machine so I don't know if I'm just missing something.