In live situations, sometimes an SM57 requires that I pull the 250Hz
down over 10dB since there's plenty of that coming off the stage, and
the 3.5kHz up 15dB just to keep up with the cymbals etc.

OUCH!

Which is why sensible people often choose different mics instead of
hoping to massacre sound with EQ.

It's hardly senseless when driving an opening band with no soundcheck.
We're talking about sound reinforcement here, not recording. Guitar amps
routinely fill small- and medium-sized rooms with substantial 250-1.5k, and
you've got to drive the high-midrange rip to complete the tone.

"Just to keep up with the cymbals"... Gotta love that. Like it's race or
something.

Last I checked it's a balancing act. I'm not one of those techs that just
says "that asshole drummer is too loud" and doesn't bother tightening up the
mix. And the 3.5kHz response can be 15dB shy of what's needed with a SM57
and a "bedroom guitar tone" even if the drummer isn't that loud. It's
better to have it massacred-but-audible than none at all, especially since
there's no guitar tone in that frequency range bleeding off stage if an
adjustment that severe is required.

Besides, I imagine the 3kHz notch of an E609 introduces the same phase
shifting problems that an EQ does.