I mentioned the obvious (that it takes time and coordination under stress to apply the brakes if your hand is currently somewhere else but on the brake control), now onto the less obvious.
I'm confused (easily done!). The brakes in a Chippy during taxi are applied with your feet, on the rudder pedals, having set a couple of notches. So your hand stays on the throttle at all times, and you can apply steering brake at the same time.
I rarely find a need to brake to stop short. On grass, when landed at the correct speed, the Chippy slows down rapidly without brake. On tarmac, one more often has to add power to keep rolling to the turnoff!
If you have over cooked it and need brake, of course it's there for you to use - as I've said before by then you'll not be needing the throttle so the left hand can be used on the lever.
Of course, if you are taxying with the usual couple of notches set and you want to stop perhaps on a downslope, paddle the rudder left-right-left and she'll stop (certainly on grass wheich is where one encounters these slopy taxyways!). Keep one foot right forward and she'll stay stopped until you centralise the rudder.