How to quickly switch power to a LED strip?
A N channel MOSFET is the obvious way to do this.  Calling this "complicated" makes no sense.  Tie the source to ground, and the LED strip between the 15 V supply and the drain.  With the right kind of MOSFET, a 3.3 V digital signal on the gate can now switch the LED strip on and off.

A candidate FET for this is the IRMLM2502.