Great post, Sans Logic (you need to change your handle to just plain "Logic"
In all my modelling years (nearly 20 years now, all the way back to the Roland GP-100), I think I'm guilty of attempting to emulate only one amp - the 70's Marshall "growl/crunch" tone just because it sits so well in a band mix by adding power without dominating the mix. Something the Ultra does so well, and others do rather badly IMHO.
But for all the different modellers and guitars I've used over the years, I've always gone for a core set of tones without any real thought about what amp and cab models I should use. My core tones my cover band work are style-based rather than amp-based:
Clean & chunky - just on the edge of break-up
Fat & full - with a little breakup
Thin & chunky - a bit like SRV tone
70's Marshall (ok, the exception as above)
Rich & creamy - more overdrive, not too bright, for a solid solo tone
Country Rock - cleanish with a little "bark"
Bright & heavy overdrive - usable for either chunky metal crunch/rhythm or boosted for sizzling solos
I've found this set of tones cover just about any song, and music style I've ever had to cover. The main advantage is that amps are out of the equation - it's just about "what type of tone suits this part of the song?"