Do you mean not using the default P0 or another prestige when leveling one of the P1-P3 prestiges?
The latter part of your statement completely negates the issues with the first part, and the point before it.
Wrt the first part:
Bear in mind many CO’s Prestiges don’t activate at all until they reach a certain level; while others are useless while leveling and only good once high/max mastery.
Karax P1 would be very bad to level with. If you’re trying to play army Karax with some static def and random maps, P1 is quite bad. You don’t get the repair beam until level 7. Level 7 doesn’t take long…except your army wouldn’t get any repair or unity barrier in P1 (Unity Barrier is a lvl 15 upgrade). Even if you want to canon-push, that’s only after lvl 11 when you get insta-pylons etc. Fenix P2 network admin(?; I don’t play Fenix) only activates at level 15. So only the disadvantage applies the entire time you level that CO; and none of the advantage. It would be pretty self-gimping (read: stupid) for someone to level Fenix P2 while using P2 (or they’re unaware). Or like Vorazun who gets Time Stop (for P3), Dark Pylon Recall and Emergency Recall (for P1) only after lvl 10, 11 & 13 respectively. Ironically, only her worst one (P2) is active from lvl 1 onwards 
The way the current prestige leveling works, I strongly disagree with giving a bonus for using the current prestige. If the bonus for leveling with the active/new prestige on Normal greatly outweighed Random+Hard bonus, then maybe it’s worth doing. I want the already-tiresome process of leveling to be as painless as possible.
Exactly. In that case, it would negate my comment above…as well as many many many people’s complaints about re-leveling, including my own.
Side note: Karax P2 is an absolute joy even while leveling up (coincidentally, it applies from lvl 1 onwards). Looking forward to using it at max mastery. Karrier has arrived!