Nobody has ever explained what regenerative shields are supposed to do, though one theory floating around is that the shield generators borrow from replicator technology and "regenerate" themselves when damaged; OTOH, this presumes that the reason shields loose power when taking damage is that the shield generators themselves become damaged, and that doesn't seem to fit IMO.
Then I'm looking over some old TMP blueprints and finding that the deflector systems on the Enterprise apparently bare the entire load of enemy weapons energy--to the point of overloading drastically--until that energy can be re-radiated back into space away from the ship. In a way you might think of this as a kind of ablative lightning rod that captures and then dissipates any energy striking the ship, and is good enough that even the kinetic energy of projectile weapons can be deflected elsewhere.
So what if reintegrative shields are similar to, say, regenerative brakes? It's a new shield system that, instead of re-radiating that energy out into space, actually captures incoming weapon energy and stores it in a capacitor for use by, say, phaser banks or structural integrity or some such? Not that this would necessarily make the shields more effective (it clearly doesn't) but it might make the ship itself more efficient by reducing the load on the fusion reactors and other power systems normally used in combat.
That's sort of what I was thinking... instead of "wasting" the energy, the captured energy and converts it into useable form.
The only real issue is... is that energy distributed to the ship as a whole or just used to power the shield system?