I would just go over the top of them, with thinner sheetrock, if yours are in bad condition, or you just cant stand them. I dont mind stomped ceilings, except they are difficult to paint, but, once done, they look very nice.

Stomped? I've heard of walking on the ceiling but never stomping. Are you talking about crowfoot ?

Yes it is also called crowfoot. Crowfoot is a lighter texture, and regular stomped is a heavier texture. My last house had stomped ceiling in every room. When we removed some soffits, I bought a stomping brush, and matched it in on the ceiling where the soffit had been. I still have the stomping brush, but, probably wont ever use it again.

This isn’t the light texture; it’s heavier.

I'd guess someone with a drywall sander could make short work of that.

If there are too many coats of paint sanding could be quite difficult. We replaced the drywall in the ceilings of our first two houses and used the opportunity to upgrade the insulation.

Materials are cheap so the cost would largely be labor. Certainly no harm in looking into it.

Stomped ceilings are very heavy texture, and it would take months and months, to get rid of all that texture, and probably some very sore arms, whether it is painted or not. Mine wasnt painted, until I painted it all because, it needed it. It has to be primed also, or the paint wont stick right to it, and I had to use a really large heavy thick roller. Stomped is not like popcorn, and fairly easy to remove. I actually like it, and would leave it.

1/4" drywall over the ceiling and you're done. You even have the option to add wafer recessed downlights.