Short answer, monsters expected to grapple can already do this (for the most part). Players and monsters with rake gain a benefit from it though.
Long answer, the balance issue will be with players being able to skip higher level grapple feats and any weird interactions with full attack actions (like haste or flurry of blows). Basically, monsters with grab can already do this. On round 3 they drop the grapple (free action) and full attack and use grab to regrapple the player (restarting the timer to round 1). All they lose for this is the +5 for maintaining a grapple in subsequent rounds (or if they wanted to pin/move or any of the other special grapple actions). Monsters with rake would also gain the free rake attacks as well. But for anything without grab (which basically means player characters) they can't use a full attack to start a grapple (there's probably an ability I've missed somewhere that does it though). So normally they only get one "attack" (instance of damage) a round, increased to two with Greater Grapple, increased to three with Rapid Grappler, increased by Constrict, am I missing any? Anyway, allowing them to full attack could singificantly increase their damage output without requiring any of the feat/magic item investment normally required to do that. Up to you if that's what you want, generally grapple doesn't need the help.
Now, this is all assuming you mean "full attack" as "multiple grapple checks to do damage". If you mean multiple grapple checks for any purpose whatsoever then everyone should grab a Tetori, haste them up, and every combat you run is going to end with the party tying up every monster involved. Could be fun but definitely a different kind of expectation.
