There are plenty of 3.3V MOSFETs that can handle serious current (and all that in a SOT-23 package - that's the downside - but they do neatly fit in between three hole of perfboard :-)). My ESP8266 is switching 40W worth of 12V LED strips without issues. Almost double that should be possible based on the specifications of the MOSFET, haven't had the need for it so didn't try.
Types I used: PMV16XN and IRLML2502. The dual MOSFET FDS9934C works fine, too, at 3.3V gate levels.