Arduino Mega support 14+ servos?

So your battery is able to pump that current.
Your ESC handles 8Amp constant with 15Amp burst.
I run 18 standard servos on a hexapod with a smaller voltage regulator.
This is what I use: 3A Adjustable step down switching voltage regulator

I bet it only pushes 3.5Amp or so. I need to get my watt meter out and see.

But I do not have 18 stalled servos pulling 1Amp each. Really, the heavy lifting is done by 3 servos at a time, with the rest of the servo pulling very little current during the rest of the cycle.