A dual MC setup gives you an extra brake circuit in case one fails (i.e., if the rear brake line bursts, you’ll still have front brakes, and vice versa). I’m too new to karting to know if this is a safety requirement by many series, but I know in the formula car world it’s almost a universal requirement on safety grounds….
And you’d be absolutely right. The second master cylinder is required for shifters by everyone, for reasons of safety. For exactly the type of situation you theorized.
I can’t think of any venue that would allow only one MC on a 125 shifter. You can check your local org. But it’s almost guaranteed they’ll say no.
Note: This is for a shifter kart of 125cc capacity; if you have an 80cc shifter, the use of a front-brake system/second MC may be optional. Check with whom you’re racing with.