I've come across it a few times, shorted transformers, never in a pinball but being a electronics tech by trade i have seen a lot of transformer issues over the years in other electronic gear. Mostly i find transformers with open circuit windings or internal thermal fuses blown, usually in audio gear, hifi amps and guitar amps.

Im yet to see a bad transformer in a pin, i've been lucky so far i guess!! though i DID once have a problem with the hi voltage display winding on my Stern Stingray transformer, where the wire had corroded where it joined onto the solder lug, but luckily i was able to repair it. I carefully scraped back the enamel insulation where the wire went into the transformer and soldered on a new piece of wire to join it to the lug, its still going several years later!!