Depends on how one architects their app on Fly.
If you rely on features that Fly clearly advertises as being in-preview or beware dragons here, then you’d do better to rely on them but with added caution.
There are hiccups and Fly comes with its own idiosyncrasies, but nothing terrible.
There are many folks who run Prod successfully on Fly. Alas, no case studies to look at, yet: Customer success stories - #3 by kurt
Of course, when you let Fly handle a lot of the heavy devops stuff, the downside is you are helpless, and have to rely on their support and eng to fix if any of it goes kaput. This can (and does) happen on any Cloud. Overtime, you can build an intuition for the kind of issues on Fly and architect your app/cluster accordingly.
What we do is, run a small percentage of our Prod traffic through Fly (~15%), with an eye to move 100% of it whenever Apps v2 is generally available. There are some sharp edges to be sure, but nothing debilitating. That said, we really only build and run simple apps (no matter the platform), nothing overtly complicated or complex.
Frameworks based on Elixir, PHP, and Ruby are among the best supported on Fly.
May be others running much more heavier workloads will chime in, too.