my 2 cents...being a club rat, many times sound checks are stressed for time and without a doubt the acoustic qualities of most stages leave a lot to be desired. During the course of a 50 minute set, sometimes the 1st song of the set IS the sound check, and many times there is necessary stage tweaking of stage amp tone and level during the first frantic moments of the set or the first song or two. I can see the value of a dedicated Parametric EQ or 3 band eq so that you can grab a couple of knobs to make quick on-the-fly adjustments. IMO, nothing is worse than that uncomfortable feeling of not being able to get your sound to sit in the "stage mix" where you're standing, and having to grin and bear it when you can't hear yourself adequately.
I see what you are saying, yet I disagree.
I also played many, many gigs in all kinds of locations, from shaky make-shift 'stages' to large size venues and everything in between.
If you have a soundcheck and an FOH engineer that knows what he is doing, messing with the tone or volume in the middle of the gig will most certainly not be an improvement for the audience, since you are most likely adressing issues that the FOH has already taken care of.
If the choice is between stage sound and FOH sound I always vote for the FOH - the audience paid money to get in and you should be able to get through a gig with less then ideal on stage sound (let's face it, it's almost always like that). I've seen bands spend more than an hour with a soundcheck only to see them crumble when it was showtime.
My band worked out a soundcheck procedure that enabled us to do a complete check of drums, bass, vox and 2 guitars within 10mins.
If the room is 'difficult' (odd sounding, boomy, shrill, etc.) you can't really do much about it. With EQ, you'd be addressing timing issues (reflective surfaces and phase cancellations) in the frequency domain, which is although popular, pointless. All you can do is run the PA so loud that the room sound won't be noticed anymore. No kidding.
It all boils down to preparation. Our admittedly rather large rehearsal space always gave us a good idea of what we really sound like as a band and we recorded pretty much every rehearsal. Zoom H2 recorder in surround mode, pick a good spot and you'll learn a lot when listening to the recordings. Once you get your presets/settings to a point where everything is audible with the vocal riding on top you know you have found your balance.
so in short (haha) extra EQ? pointless IMHO. Fix it at the source, at the right time - not right before or 'gasp' in the middle of a gig.