Overkill, just skim coat the wall with drywall mud, prime and paint.
Depending on your skill at mudding, this can be easy or a real dust storm
(due to the need to sand out your mistakes). Even if you put up new
drywall, you would still need to mud the seams (maybe not the whole wall but
I still think that would be a lot more work and expense).
In most cases you do not even need to prep the wall before mudding but if it
had a very glossy coat I would sand/ score or prime that.
A little sanding beforehand to knock down the tallest peaks of the texture
will save you a lot of time and material trying to bury them.
SInce you'll be making a mess, get rid of that popconn cieling if you have
it while you're at it.
Another option, put a second layer of drywall and mud normally. This would
add sound proofing to the room which may be a desireable trait dispite the
extra cost and effort.
I faced the same deal here - basement walls that some genius "textured"
with a roller and a bucket of cheap paint. The same yahoo taped the
joints and his handiwork was popping loose in several places. We decided
to just rip it all down as the work involved with skimming and sanding
would never fix the bad tape job hidden under all that goop. If you
don't have much experience, hire a pro as it's often cheaper and quicker
to let them put up the wallboard and finish it.
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