Would there be a problem installing 20A outlets/receptacles on a 15A circuit?
I'm going to be plugging in a 14000 BTU portable air conditioner and it just seems like a good idea to have a 20A outlet to reduce heating in the outlet, even if the circuit is rated only for 15A.

That won't have any effect.  The internals of both 15A and 20A outlets are made of exactly the same stuff.
That's due to a UL requirement that 15A receps must be able to carry 20A internally, so they can be used in 20A circuits per 210.21.

If anything, 20A outlets are a bit worse, because the neutral wiper cannot be ful-width, since it must have a notch in it for the 20A sideways neutral.  Of course many 15A receptacles use the same stampings.
Putting a 20A recep on a 15A breaker would defeat the entire purpose of 20A plugs being a different shape. So obviously that has to be a code violation.  You don't want to plug a 20A-requiring appliance into a 15A circuit, because it would definitely overload, and ALL safety margin would rest on the breaker tripping.
If you wonder why a &quot;single point of failure&quot; is a bad safety strategy, watch aviation accident investigation videos.