If you add two frequencies together, you get four frequencies:
100 + 10 gives you:
100
10
110
90

If you add two frequencies that are close together, you get:
210+200=
210
200
410
10

If you put your signal through a mixer you can pick which frequency to work with after the mixer.

If everyone who designs radios designs their radios to mix signals and come out with signals on 10, electronic circuit makers can design circuits for processing signals on 10. You buy premade modules and plug them together. Cheap easy, convenient.

Mixers bring radio signals that could be on a wide variety of frequencies to a single standard frequency. It would not be 10, with 20 mHz wide channels. But that's why they do it.