How does a speaker blow out?

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.    

What Erik said (regarding clipping), but: after a x-over passes that high freq distortion to the tweeter and burns it (typically: open), the energy that no longer has a path that way, is routed to the next highest freq driver, in the circuit.

True, but since most crossovers are in parallel, the HF voltage seen by the woofer remains the same. More likely to burn the first coil in the low-pass filter than the woofer itself, but things happen. :)

The amp having less current draw due to an open tweeter circuit could mean a higher voltage though. 

In my case I blew my Tekton impact monitor tweeter because I got so involved with the classical music Iam playing , I turn the volume too much more than the speakers can handle, first distortion then I smell like something is burning. Iam glad Van L Speakers here in Chicago able to fix them.