The main concern with open top cages is strangulation. A parrot can open it a little and get their head through, the top then closes back up, often with the parrot holding it closed by their weight, and they hang themselves.
I have a open top with a latch that doesn't do a good job, I have it securely closed with zip ties.
I have a couple open top cages and have also secured mine with zip ties. The top didn't feel real stable and it's nicer to have a separate perch or playgym than wedge a perch in the top each time you open it.
LONG ago I purchased a cage that could have been opened on the top, but I opted never to use it, as I was afraid it would weaken the joints where the top portion opened up (held open by an additional perch), and could then potentially hurt my baby.
Remember, birds are VERY very smart. It's like "monkey see - monkey do". They see you open/convert their cage, and the next thing they will try and maneuver their own adobe.
I do not see the point of having an open top to begin with. All it does is give it a higher place to perch and more difficult to get down into its cage when you want to put the bird back in the cage.