My red lorried
amazon, Alura, has been with me for over 30 years now. She doesn't fly much, but as with any parrot, there's a bit of dust from her feathers. No big deal, never impacted my aquarium. I've no worries that she's going to land in my tank... but I'd laugh my rear off if she did
I tried, hard, to run a topless aquarium. It's a long, fat, low tank, with a bar surround, and a high, hanging lights. It looks way better with no top. Defended my decision on several occasions, but eventually, I gave it up. Bought a clear framed screen top from Octo Aquatics. Expensive, but it looks great, and I haven't lost a fish since.
I may one day run an open top aquarium again... but if I do, it'll be stocked with pipefish, box fish, bottom dwelling scorpionfish, anglers, etc. Fish that simply can't generate enough speed to jump out of a tank
Short of that, nope, I can't recommend topless.