Make sure the semi gloss is latex paint. I suspect it isnt, since latex paint doesnt go over popcorn very well. Since its painted already, you can use whatever kind of paint you want, but, I would put a coat of primer on it, just in case its oil based paint, so you dont end up with a peeling ceiling. Most pop corn ceilings are not removed because they are dangerous, they are removed because people want flat ceilings. If you dont mind the popcorn ceilings, then keep them, and paint them, and stop worrying. You may not even have asbestos in your popcorn. Not all popcorn ceilings did. In any case, you are not going to have asbestos floating around.

Thank you! I was just running down the list of things I could worry about before I try to fall asleep and this bugger popped up!

I'm not understanding the issue with washing and painting your kids.

On a different subject, it would be good to reno your popcorn ceilings.

HAHAH 🤦‍♀️

As others have said I don't think there are any safety issues with leaving them, even if there is some asbestos (since you're not going to be banging against them or anything like that).

On the other hand, installing lighting could be tricky if you're moving existing light fixtures around -- some drywall people do a good job of fixing the holes and re-texturizing to match the existing popcorn, but it's easier with flat ceilings.

The best way to avoid removing cottage cheese ceilings, is to put drywall right over the top of it.