There are a TON of pre-req feats that do nothing for later feats in a chain. Combat Expertise being an obvious culprit. Using that feat actually makes every other maneuver worse. Same with Power Attack. (since all penalties on attack rolls apply to maneuvers)
Tripping Strike has Imp Trip as a pre-req, and the reason behind it can be anything.
In order to trip, you normally have to sacrifice an attack, in this case you are so good at it that you get to do it for free anytime you land a particularly good strike (crit).
However, as an add-on, it doesn't get its own roll with attendant bonuses, you just trip exactly as well as you crit. Whatever that number is.
In the same manner that I wouldn't expect to add another +6 to my Bullrush total from my shield slam (+4 feats, +2 Dwarven racial sub for stability), I wouldn't expect to add my bonuses from my feats to an add-on trip.
However, if that is the ruling handed down, it just makes my characters better than I thought.
I miss worded that earlier statement. Of the Feats I've read the Prerequisite and subsequent feats have a way of interacting directly with each other, whether it's making a bonus/situation stronger by stacking effects or by mitigating penalties the original incurs.
In the case of Combat Expertise and the Improved/Greater Combat Maneuver Feats:
While using Combat Expertise by taking a -1 penalty to melee attack rolls and combat maneuver rolls you gain a +1 dodge bonus to AC. When your BAB reaches +4, and every +4 thereafter, increase the penalty by -1 and bonus by +1.
So by giving up your offense you gain an equal defense.
Now let's use Trip and Bull Rush for my next part. The Improved and Greater forms do 3 things. 1) The modify what happens during the maneuver by first having you not provoke an AoO from the target then later making your target provoke an AoO. 2) Your CMD against the maneuver in increased by +2. 3) You gain a +2 bonus on checks made to Trip/Bull Rush with Improved and an additional +2 with Greater.
So with Improved and Greater we have a bonus to mitigate the penalty from Combat Expertise as well as boons for the offense with a bonus to defense.
It seems like too much of a step backwards to not apply the bonus to the strikes because even without Combat Expertise active the Strikes are already at a disadvantage by having to use your bonuses to hit with your melee attack which, more often than not, is much lower than your CMB.