Powering a mechanical (el. magnet) doorbell with an AC LED driver
Probably your doorbell requires AC at 60 Hz frequency; to save weight
and cost, an LED supply might use a high frequency (50 kHz) and very
small transformer to power LEDs, but this will more likely demagnetize
the doorbell's moving part than it will drive it.

A classic doorbell magnetizes the iron part with electric current,
taking about 1 millisecond.   Then it reverses the polarity a few
milliseconds later.   But, it's usually completely magnetized while
the AC is switched on.   That same doorbell, with 50 kHz excitation,
will only achieve 1/100 of its full magnetization before the electricity
reverses and tries to magnetize it in the other direction...