The only times I have used feigned flight, the Romans had enough PIPs to be able to hold their line each time. The problem is that the foot never follow-up against the mounted, so its difficult to pull them out of position.
I've tried it with LH(F) who are similar against the Bd to LH(S) if you double rank them, but I kept running out of PIPs to put them in with. The problem with them is that the Cv(O) would come out and murder them. With LH(S), there is a very good chance that they will murder the Cv(O), so its more risky. Charging the Kn(F) into deep and/or supported Bd is going to result in a lot of dead Kn - you need to keep the Kn to kill the roman Cv(O) or go for Bd who are only one deep. Otherwise they kill the front guy and pursue in to be double overlapped. Don't forget that LH can always opt not to follow-up and Kn don't have to follow up in the enemy bound except against other Kn.
The LH(S) will whittle down the Bd in the end, but it will be a slow process. the Art are a real pain, but if you get close enough to the Bd line they can't shoot overhead. Go for the the flanks, especially if they are anchored in rough terrain - LH can move through rough quite rapidly.