Caps on the battery side of things allow the system to deliver more surge current (hard acceleration, for example) without the voltage dropping off (killing top speed, and causing heat.) I'm thinking the MurfDogg Octane Booster is something like this. A big bank of EDLC's or the like.

Caps on the BEC side do the same thing. Your servo tries to pull a ton of current out of a 3A BEC, and weird things will happen (Brownouts, glitching) when the voltage starts to plummet when the load exceeds the BEC's capability to hold the line up. This also causes heat, because the High Side Driving Transistor in a switching arrangement will be working overtime to handle it.