Just because a tweeter still makes sound doesn't mean it is healthy, and it is impossible to judge the performance of any portion of the intended bandwidth of the speaker without the whole bandwidth playing.
To test drivers' health you need to measure the electrical impedance of the speaker and/or the drivers using a tool like DATS.
Also measure the acoustic frequency response of the whole speaker to quantify what the "dull" sound really means, using a tool like OmniMic.
Post this data for advice on what might be wrong, but it will probably be rather obvious.
It is unlikely that any signal within the power rating would damage Tannoy crossover.
Often seemingly disconnected circumstances are actually connected. And seeminingly unconnected circumstances are not related. Something else that you didnt notice may have happened that you blame on the test signal. Or the test signal damages sometimg else besides speakers, or speakers arent really damaged.
You have to use scientific method to test and prove to know what's really going on.
Swap in different components, cables, check connections, etc. dont assume anything.
I once blamed every components in my system over a yearlong period for a random ticking sound coming out of the left speaker, or so I thought. It turned out to be nail pops in the wall behind the speaker when the sun hit that part of the house in the afternon and again at night when house cooled. It took a year to figure it out because I was stuck on "it's coming from stereo system"
