I think that is why по- is so often used as the perfective-adding prefix - its meaning already is shortness.
In that sense, попить might be the more natural counterpart, and выпить is merely the more functionally common perfective realization of пить.

I guess you could say that you start with the base meaning БИТЬ, and it gets fragmented along many axes, one of which is perfectiveness, which itself gets split by prefix-axes, being the different kinds of added conceptualizations. So in some cases there are various aspects of perfectivity stressed in different prefixed-versions of the base, as well as different added meanings altogether stressed.

I suppose the reason prefixes all make perfectives, is that they each bring to the table the idea of an action вы-out of, у-away, etc. and those actions are inherently whole ideas, such that if you add the whole idea to a root, you get the meaning of the root carried out across a whole concept; and from THERE you have to distinguish that the desired meaning *also* involves duration, so the infix is added.

*representing an endpoint, a finished verb product

ROOT* (пить)
(xxxxxxxxxxxxxxxxxxxxxxxxx--------по- instantaneity----perfective--*xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxx/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(---Simple Perfective branch--xxxxxxxxxxxxxxxxxxxxxxx------added infix-- repeated completion----*xxxxxxxxxxxxxxxxxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxx\xxxxxxxxxxxxxxxxxxxxxx/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx
(xxxxxxxxxxxxxxxxxxxxxxxxx----------вы- completion-----perfective--*xxxxxxx----------added infix----------imperfective----*
)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(-------some prefixed meaning-----------------------------------------------------------perfective----*xxxxxxxxxxxxxxxxxxxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx
(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx----------added infix----------imperfective----*xxxxxxxxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx/xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x
(-------some prefixed meaning-----------------------------------------------------------perfective----*xxxxxxxxxxxxxxxxxxxxxxxx
)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx
(ad nauseum




For some ROOTs, the perfective branch contains only one descendant, which employs all aspects of perfectivity? I think probably.