In both the single STOL situation, and taking off in a piston helictoper - or for that matter flying over, say, forests, in either, one is frequently in situations where an engine failure at an inopportune moment could cost you very dearly indeed. The scenario you paint, in terms of a STOL takeoff in a twin, doesn't seem entirely dissimilar, to me, than that of taking off in a single – EXCEPT for the VMC issue.
I think the difference is that in the single, in the case of a non-catastrophic engine problem, you leave the throttle fully forward and fly the aeroplane. You probably look for somewhere, or a selection of sites, to put it down straight ahead. If you're still climbing, bonus, the engine failure wasn't as bad as it might have been and you keep climbing. If the engine loses power completely, you're going to glide to a landing site as best you can.
In the twin, you really have the decision to make, right then and there, before you have much chance to properly assess the problem. If you don't make the decision to close both throttles, and the engine goes on to wind down to complete failure, you're flying yourself into a loss of control.
By contrast, in a similar situation in the climbout at Vyse or above, you have a little more time to assess the situation, and, just as in the single, can afford to leave the problem engine running to see what happens. Of course you can't wait forever, but you're not going to shut it down at the first cough at lowish level if there's a very good chance that it will still be producing useful power.