Why are so many RF remote boards relay-based?
Relays have the advantage that they offer complete electrical isolation between the controller and the load. 
The relay can be used to switch low-voltage signals or mains at modestly high currents.
Relays make a nice clicky sound.
Relays are reasonably cheap.




Figure 1. Solid-state equivalents of the relay boards are available by the million too.

The solid-state boards use opto-isolation between the logic side and the load to provide a similar level of insulation to the relays. Their advantage is that there are no moving parts to wear out. Their disadvantage is that different types are required for DC and AC switching operations.