Proportioning Valve

A soft pedal can be either or both, a hydraulic, or a mechanical, issue.

As to bench bleeding;
The reason we remove the MC to the bench, is so you can angle the front down, so that the air will come UP to the compensating ports, and exit into the reservoirs, when you tickle the pistons; AND so you can install those little short hoses to return exiting fluid back into the reservoirs; firstly so it doesn't make a mess, and secondly, so the MC doesn't suck air in from the discharge ports.
Yes, you can angle the front up, it only takes more pumps to purge the air out the other end.
So;
It is possible to "bench bleed" it on the car. But it's probably just as messy,lol.