Rebuilt Mechs come at the same level as the enemy you destroyed. Usually, your strongest mechs will be at a similar level as your enemies so this is really not much of issue. Also, the player has items and weapon upgrades available while enemies don't (this will change in higher difficulties), but since they come in large numbers, there definitely are quite a few challenging areas to come. That said, once your Mechs gained some extra levels, early areas will unavoidably become trivial, unless you go back to grind your low level mechs.

And to clarify, you don't control three Mechs at once. You build a squad of three Mechs, one of which you control at a time, but if the situation calls for it, you can switch in another one on the fly.