Simply because, as you stated yourself, thrust = mass x velocity². Increasing the velocities (into the Mach numbers) increases thrust...
The theory and work involved in creating a variable nozzle going beyond Mach 1 would be outrageous, though...and would have to be preceeded by a nozzle getting it up to 1.0 in the first place.

Be an interesting project...however first i need to get my other projects off the table, which may very well last a few more years at my current rate...

Hank