Sooo many things in here....
You won't accelerate if you hit the throttle to rev match and let the gear back in, it's just a matter of revving to the point just below where it needs to be, so that as you react and let the clutch back out the rpms fall to just where the wheel speed is. (Unless you have a 0 reaction time because you're a robot)
The reason to let the clutch out in every gear while racing is an extra margin of safety. If you overheat or lose the brakes you at least have some compression braking to slow down a little, you're also in gear more often and have power to the wheels to make a correction or avoidance move if needed. The transmissions on race cars often don't like skipping gears either, and some varieties (sequentials) can't really.
Not having ABS isn't really that big of a deal, I can stop my car without much quicker than the car with because of how it's set up. You're also not really pumping the brakes, you're only slightly adjusting the pressure of your foot, so moving 1/16th of a inch maybe cycling between close to lockup and letting off a bit.
Add in cars with worn or no synchros and you have to try to double-clutch to get the thing to go into gear while doing heel and toe. I still can't do that quite right, but I can heel and toe to rev match the car with good synchros no problem. Double-clutch heel and toe goes: clutch in, shifter to neutral, clutch out, throttle to match speeds, clutch in, shifter to next lower gear, throttle to match speeds to wheels, clutch out. Doing that while braking with the same foot is hard.