Is it common to solder copper pipes under a kitchen sink, or is it almost
universal to use compression connections there? If you found some already
soldered there, and wanted to put new connections in, would you use a
torch
to remove the old ones, then use compression connections for the new ones?
Or what?

Don't know about common, but I hate compression fittings.
Everytime I have to turn a valve attached to a compression fitting, I worry
I would disturb the fitting and cause a leak.

I did put in solder fittings under a sink. Just had to make sure there are
no plastic pipes nearby and put metal shield on anything that burns easily
(wall or cabinet).

Especially if pipes come out of a concrete slab foundation, and only stick
up 2 or 3 inches, so there is not much excess pipe length to cut and start
over.