Since I usually play vs the AI, I can't really comment on carrier spam - except maybe for the fact that I use it myself.
Against carriers, the trick is to survive the first wave and decimate the strike crafts. Many people forget that strike craft need quite some time to be rebuild... So once the destruction of the enemy strike crafts is achieved, the carriers are sitting baits - except for the fact that they will try to run away.
Okay, so how can I destroy all these strike crafts?
Well, you can use flak frigates. Mass them, set their move-to-attack radius to minimum range and gather them around your fleet. The enemy may micro his fighters to avoid them, but if you stay tight, you can easily adept.
But frigates are only the minor part to deal with mass strike crafts - the choise of caps will decide the game. As TEC, you have to use Magnetise, as Advent, you rely on Telekinetic push (which WILL rip the strike crafts to pieces, esp. if you got more than one carrier), as Vasari... Well... Okay, dunno... Phased out hull?
Remember to turn off outocast! You have to wait until enough enemies are within range and THEN trigger your abilities. You might loose your caps - but if the strike craft go down, the rest of your fleet will make micemeat out of his carriers.
Another thing is, that YOU have to choose carefully where to fight.
On the offensive, your choises are limited. A pack of charging cobalts might do the trick, maybe Illuminators if you can jump in close enough, as Vasari, a Marauder might speed you up enough to catch them.
However, on defence, you can win! With phase jumo inhibitors, he can't run away. And if he targets them with his strikecraft, you have time to catch up and kill his carriers. And don't forget that inhibitors do now stack. 2100% jump time, anyone?
I agree it is tricky and micro demanding to deal with mass strike crafts - but is not impossible to win.