I do most of my flying with a PSII controller with a 1250 mAh 3s LiPoly battery inside. I will usually, after a flight, have a starter/igniter where there's a little ball of formerly melted metal at the spot weld between one end of the bridge wire and the clip leads...pretty much whether it's an older Solar igniter or one of the more recent Solar Starters. I suppose it is possible for it to burn out so quickly that the motor doesn't light...but it seems that would be difficult if the thing were against the propellant as it's supposed to be.
Having too high a voltage is, however, definitely an issue when trying to use a Sonic Igniter in a White Lighting motor. They will pop too fast on a 12V club system and not get the motor lit. But using a Sonic on 9V (as a stock PSII controller uses) works better.
The Solars were introduced in 1972 with the Solar Launch Controller, which was the first 4-AA cell launch controller from Estes (though the Electro-Launch could be configured with 4 D cells), so clearly the bridge wire was originally sized for success on 6 volts and moderate current capacity. But even back then, alkalines were the way to go, not carbon-zinc cells.