How does a speaker blow out?

Harbeth SLH5 (original, not plus)

        Gotta love those pedal notes!

        Especially, on a Direct To Disc recording.

Organ music can be pretty demanding, but it seems something’s amiss. I’m running a pair of KT66s in triode that produce in the 10-12 watt range, and am able to power 89db sensitivity speakers fairly loud in a large space, Granted I haven't fed them low pedal notes lately.  Tubes typically break up pretty gracefully without causing damage. I do have an active subwoofer to augment the bottom octaves, but the mains still run full range without issue. What model is your amp?

Yes, low power amps go into clipping when trying to drive speakers unless the speakers are very efficient, i.e. Horns.

Also, tweeters: IF the tweeters are not capable of sudden bursts, like the Dynaudio D21’s, their voice coils can melt.

These days many tweeters have ’ferro fluid’ which can absorb the heat of a burst, thus the coil does not melt.

Example: amp on wrong input. Volume jacked up, then, switch to correct input: that high volume slams the tweeters coil.

From my experience too low power (ie HF clipping) is generally the culprit behind tweeters failing, but over power (possibly LF clipping but certainly overheating the   voice coil ) is why you blow woofers.  Subsonics can often be the mysterious cause of over output in LF.  Curious  this happened on notoriously difficult  organ material.