If the "USS Enterprise" takes the "Best of the Best".
I guess the "USS Cerritos" gets what is left after everybody else has been chosen?
This wouldn't necessarily work like that in Trek.
Starfleet Academy does have relatively high standards, so its highly unlikely that you'd end up with really low quality people en mass (or at all - and if you do, the number of 'low quality personnel' would be exceedingly small - and they'd be dispersed throughout the fleet, not all packed onto a single ship - its also possible that if some people are of 'lower calibre', they are usually put with other more experienced officers so they could learn from them).
In Voyager, we've seen from episode 'Good Shepherd' that there were about 3 people (out of a crew of 150) who were described as 'misfits'... but this was mainly because they never went on an away mission.
One however wasn't particularly bad (Harren I think)... had really high aptitude in theoretical physics, but serving on a starship for 1 year was 'mandatory' to get into a designated Institute... but otherwise, wasn't incapable or 'worst of the worst' - in fact, if Voager didn't get stranded, he wouldn't even be on a starship after the first year - but might have been transferred when the Dominion War started.
As for the other two... Celes (who had issues with reading sensor data and generally dealing with algorithms) was an oddity... the fact that she passed the Academy on 'benefit of the doubt' (because of Cardassian occupation of Bajor) seemed 'iffy' at best - I fairly doubt Starfleet does this for people on a regular basis (she would be an exception rather than the rule).
And the third one (the hypochondriac - Telfer I think)... well, to be fair, he didn't seem incompetent at all... just lacking in overall confidence (heck, even Barclay was comparable to him, and Telfer managed to solve his issues in a single episode - all it took was a dark matter life form to invade his body temporarily

).
The Cerritos is more of a parody... but at the same time is supposed to be canon?
It just seems so vastly contradictory compared to what we saw up until that point from Trek as a series... and doesn't strike me as something that would WORK as part of Trek canon.