I did, once. I started putting Painted Fire Red culls in my favourite Betta's tank, because I thought he was too mellow to eat them. The shrimp bred quickly and the Betta stuffed himself with baby shrimp- I'd see him eating them frequently, and for a while I thought it was free live food and he'd be fine, but then his belly swelled. He died of bloat 11 months after I bought him and about four months before the shrimp went in (I drained the tank to remove the shrimp about a month before he died, but it was too late).
My Bettas usually live a lot longer than 11 months. I still have shrimp and I still have Bettas but they will be kept in separate tanks from now on.
That said, adult Amanos may be safe because they are large, but I've heard anecdotes of them deciding to make lunch of a Betta's fins while it rests. (I'm aware my story above also counts as an "anecdote").
One of the reasons Bettas are so popular is that they have some personality; but that means they vary a lot in temperament, - hence the different opinions out there. People have different experiences with different individual Bettas. I would only try it if I had a spare tank ready in case I needed to separate them again.
That's interesting. I had a pretty chilled out betta in a well planted tank full of cull cherry shrimp I felt too bad to cull, but who had started breeding like mad. So I took the cowards way out and thought I'd try a betta knowing he may help with population control. He'd stalk them fairly unsuccessfully while I was watching. No doubt he ate a few, but I believed most managed to evade the betta.
However, at 7 months he swelled up and developed drospy like yours did, without any particular reason. I'd never even considered the shrimp diet as a reason for this.
The other thing I should add, I didn’t see my four Amano shrimp for 4 months. Literally they would sneak out at night to try and feed. I only knew there was some in the tank from moult shell. What ever about the shrimp evading the betta, If he hunts they will always be on predator alert and unlikely to display. I won’t be keeping them together again. As they say I have lived and learned.
I get that you are in doubt of what happened in my tank, but deliberately feeding shrimp to a fish, one at a time, is not the same as an endless buffet of baby shrimp with no human hand involved, except when I finally removed the shrimp.
The Betta tank in question is six inches to my left for most of the day, so I actually was right here observing what happened. The number of adult shrimp didn't increase (except when I added more culls), but they were breeding like mad as cherry shrimp do, and the Betta was eating all day long.
I'll admit that it's possible that the endless gorging was somehow unrelated to the bloat, but losing a Betta in less than a year is not normal for me, and I will not keep shrimp with Betta splendens in future.
My betta ate rcs size shrimp indiscriminately and terrorised a full grown amano into constant hiding / jumping if you put them together - it constantly tried to hunt and kill it even though it can't swallow it whole.