heres a perspective...(mine
Unless the Engineer has rehearsed with the band extensively and been part of the creative process it is NOT the engineers job to decide how the band sounds. Instrument tones (including Drums) are the responsibility of the band, as are dynamics, solo levels, vocal balance (obviously not the band/vocal balance, but the balance between vocals).
The primary job of live sound enginere who works for the venue or the sound contractor is to safely run the system while ensuring that the FOH and Foldback EQ has removed any resonances and is appropriate for the venue.
Once that factor is under control, their next job is to try and balance the sound in an attempt to replicate what the bands intentions are. This is informed by the stage mix....If one guitarist is much louder on stage then the other then the only reasonable conclusion an engineer can draw is that the FOH mix should also have one much louder than the other.
On the issue of EQ....For Drums it is reasonable to expect the engineer to find and reduce any resonances that are clouding the kit - but initially it is the drummers job to arrive with a well tuned kit. For guitars the FOH sound should match what is coming out of the amp...Basically any other changes should be approached extremely cautiously by the engineer.
Now obviously, good engineers will have both the venue and the bands best interest at heart and will then build on the platform as described to enhance and refine the mix to give the audience the best possible experience. This may include subtle EQ and FX...and most importantly maintaining a good balance. (I am old school...if the engineer does not have a finger on the lead vocal fader the whole time there is singing they are either lazy - or there is too much compression
....or, OK, the singer might be a well rehearsed profesional.... )
I am fully aware these views may seem odd.....and of course all of this changes if the Engineer is essentially a member of the band. I can say that I applied this approach very successfully when working with experienced musicians to great success with many industry folk coming to celebrate the gigs sound with me.