All of my aquariums are open tops for best light penetration to plants and I like to use cuttings from my weeping willow trees and allow them to root out-I love the look of the flowing branches sprouting from the tank-
I generally keep the water level pretty high on all of my tanks too and haven't had any issues with fish jumping out-Even on the grow out tanks with 30-40 swarming juvies following and jumping out of the water at you anytime you get close to the tank..lol...I am sure I have had a juvie jump out and die or be eaten by one of the cats-I just have never seen any bodies and I usually have too many to count to know if any are missing in a grow-out tank anyway-
I do have water lettuce and frogbit that covers about 25% of the surface and IMO/E the floating plants do help make the fish feel more secure-Usually the reason a fish jumps out is due to fear when its not water quality related-The fish is running from another fish or startled by something that makes them run then jump being part of its defense.
I have had the top of the tank covered so dense with floating plants with the frogbit getting deep and have not had any issue with a Betta not being able to get to the surface for air. My outside tanks especially are covered from edge to edge with frogbit and water lettuce-There is more air space among the floating plants than you realize-I have never feared for my fish suffocating due to the dense floating plants or them jumping out due to no tops.
Even with the outside tanks and rain as the tank overflow and flush out and we have had 3-6in at one time this year on several different occasions and I didn't have any fish loss with the adults-I did have a couple of nest with eggs get washed out and I am sure some of the smaller fry got washed out too-but none of the adults.
A Betta can jump out...mine never have with my open top tank or suffocated due to dense mats of floating plants-