High Wing Drifter
I have had a near refusal of an engine to run on carb heat "on", but it was in extreme circumstances, on a a Harvard, P&W 1340 cubes, 650 odd bhp, OAT about 35deg, field 4000ft amsl.
This was at the end of a simulated forced landing, and on opening up the engine just coughed and spluttered until the carb heat went back to cold. And, no, it was not caused by too rapid throttle opening.
I have also heard of a case of an aircraft having engine cut-out on takeoff following carb icing on a long taxy out.
Moral. Most of the time everthing is OK. Just now and then you get bitten.
Regards, Dick W