Keep in mind that exactly in the times where you get multiple broadcasts, you want the service to be spread. If there's 10 broadcasts in a minute (likely on the way to the anchor spot in TPPH 3rd room), it's much more important that everyone has SOME cap to get them moving RIGHT NOW, than getting anyone up to 70%. That mach with low cap skills can burn to his anchor spot just fine on 2-3 cycles from 1 basi and just regen once he gets there.
Approaching your proposal from the other side: a cycle from a T2 transmitter takes around 3.5s after boosts (sorry, don't have the exact numbers here at work). 3 cycles would take 10.5 seconds. If there's 10 broadcasts, it would take 105 seconds (i.e. over 1,5 minutes) to get to the last their cap. (probably more, because server ticks probably add 1-2 seconds to every switch-over for every basi, so closer to 2 minutes). That's way too long for someone to have to sit on a beacon...
I could see this work great in a fleet op optimal ships with high-skilled pilots that know how to manage their cap and can keep fighting down to 10% cap and then have enough to coastto their spot. But in a fleet where that's true for only half your pilots and some of the others are Rokh and Maels who, at 30% cap are 2 MWD cycles away from capping out, it's probably won't work that great.
And like Malcolm just pointed out, it's a way to clear kinda-sorta clear the worst of a backlog when stuff gets out of hand.