Walls and Ceilings - Low Sagging Ceiling

The ceiling in my kitchen is only 7' and it sags; making it look even lower. The ceiling is textured with what I think is "stippling"? A small section of the texturing has fallen off and it looks like the ceiling is covered with sheets of plywood. You can see most of the seems as well.

I would like to tear the ceiling out and re-do it with dry wall, but I'm afraid of what I might be getting into. What would be the purpose of covering the ceiling with plywood?

How old is your house? Do you have an finished upstairs above this ceiling? You might be mistaking plaster that has aged and yellowed with plywood. It might be this plaster that is actually falling off the ceiling. Or you may have some ceiling joist issue. Taking down your ceiling will be a huge mess but I don't think you will get in over your head.

are the ceilings in the rooms around the kitchen also 7' high?

All of the ceilings in the house are 7', and most sag or you can see the seams. What has come off of the ceiling is thin; it kind of looks like the thickness of a few coats of paint. That's what made me think that it was stippling; that and the texture.

The house was built in 1927 and was worried that it might have asbestos in the plaster; hence the plywood, rather than drywall.

Oh and there is nothing above the ceiling, just the attic, which has blown-in insulation and does not have a floor.

You have plaster ceilings and that need to be replaced. I'm not sure why you have 7' ceilings in your house. Usually houses of that era had tall ceilings.