I agree. You can certainly teach them not to scratch certain things,
but part of that process is finding something that they wll enjoy
scratching.

The OP mentioned that he had tried some things, but he didn't give
much detail.

The carpet squares were probably useless as testers.

Most cats prefer a vertical service to scratch or a large horizontal
one. And they want it to be secure. A small carpet square will move
when scratched, and won't be as attractive.Also, the type of surface
makes a big difference. Cats have individual taste.

For example, Maynard prefers vertical wood (tall cat tree with wood
base)  and occasionally uses the cardboard floor scratcher (a round
flat thing with cardboard in the middle).

Chase loves the cardboard as his favorite and also likes the vertical
sisal post.

Neither of them scratch on carpet or furniture.

Kira prefers rug and fabric. And she prefers horizontal. She scratches
on the top shelf of the cat tree, and the seat of my kneeling chair. I
accepted that loss many years ago, and she has compromised by not
attacking any other piece of furniture. She will occasionally take a
swipe at another chair seat, but a simple "no", and she quits. She
occasionally scratches at the vertical carpet post, but usually just
uses it to stretch. But if you take a roll of carpet and lay it down
(horozintal), she will be all over it in a heartbeat. I have a couple
rolls of carpet stored away, and I keep them in plastic to protect
them.

There are some really nice cat trees these days. I would recommend
getting one that is at lesast 4 feet tall with some tall posts so they
can stand up, really stretch, and get a good scratch in. The trees
that have wood, sisal, and carpet are the best. No matter what each
cat prefers, they can find something suitable. Justmake sure it has a
good sturdy base and doesn't move much. A dinky cat tree that doesn't
allow them to stretch or moves when scratched, will be an ignored cat
tree. Figure out what they like, and they will like it more than your
furniture.

And sometimes, you just have to compromise. Once Kira ripped the seat
on the kneeling chair, I considered it a lost cause for that* chair.
She is worth me to me than a stupid chair, so it is her chair now. I
have since gotten a new chair for me, and use that one only as a
spare. She sits on it a lot. And I don't discourage her from
scratching that chair. She knows it is hers, and mine is mine.
Sometimes, we just have to come to an understanding and we can afford
to give in on occasion. We have to choose our battles.

Find something for the cat to have that is theirs to scratch and
destroy as they want. And once you know they are satisfied with that,
then get your new couch. you might want to start with a cover on it
until you are sure they understand the rules on the new couch. And
just reward them for scratching their furniture and being good to
yours.

Whenever I see my cats scratching their post, I give them a "good boy"
or "good kitty".