Is really that hard to tweak an amp?
Fortunately, I've had the good fortune when recording rock the past number of years, to go to a couple of studios in Los Angeles that have great selections of vintage amps, and in some cases, guitars-at no extra cost.
If I'm in a hurry (which is almost always), I'll grab 2 or 3 guitars and amps in addition to what the player has for shoot out purposes.
I have the player "audition" the part live in the with his/her usual setup. Then, I make a decision to maybe try another guitar and maybe one or two other amps to check out. This happens fairly quickly: we just try a few bars with each amp and each guitar and make a decision. Sometimes, this might inspire layering of different guitar/amps. I like to keep things moving because I don't want the player to get burned out.
I'm also a big believer in getting it right at the source. Assuming the guitar, amp, Mic's, and placement are right, after adjusting the balance of the 2 Mic's (or 3) on the amp, I always make EQ changes with the tone controls on the amp rather than EQ'ing in the control room. When it's right, it's right.
I've only recorded a guitar direct when I wanted a specific effect, such as the signal going in to a super long reverb and only getting the reverberated sound. While I've used things like The Pod, Sans Amp, and the like, I've found that the player has to have really great tone in their playing to get even a decent tone out of those things.
Cheers,