I can't say that without seeing it.
We had a "motor failure" that I traced to the centrifugal clutch
that OPENs the connections to the start capacitor once the
drum starts moving.
We had an ACbrrr fan that wouldn't "start" that I traced to
a bad motor cap. etc.
I.e., if YOU are trying to troubleshoot the problem, it's
one thing I would look at (relatively inexpensive) as it
could explain your symptoms.
It could also be a loose belt/tensioner pulley.
Or a bad clutch switch (if the motor uses one).
Or a bad motor.
etc. It's relatively easy for a technician to lump every
related issue into a "bad motor" diagnosis instead of
identifying the specific cause.
[And, chances are, if he replaced the motor and it still
didn't spin, he'd claim you ALSO needed a start cap! When,
in fact, that may be ALL that you needed!]
Being an electrical engineer, I tend to look for electrical
fixes first (less involved than mechanical ones!)
If "still new", do you have warranty coverage? Note some
credit cards will double the original warranty if you purchased it
with plastic (worth checking your records).
Bottom line is YOU have to decide what your time is worth
(money, aggravation, etc.).