Why aren’t there more tricycles with rear disk brakes (between the two rear wheels)
Check out the Atomic Zombie plans for "deltawolf"    These are do-it-yourself plans, they don't sell completed bikes.

Here's someone's bike from the rear



There's nothing to stop you putting the caliper mount further out for a 180 or 203mm rotor.  You could also set up the same on the left-hand axle.

Note this design is a single driven wheel rather than a solid axle or a differential.

Someone's build: http://atomic-zombie-extreme-machines.blogspot.com/2010/08/building-deltawolf-recumbent-speed.html