1. that would, IMO, be a band decision. Not a you decision.
If the band is ampless, and you insist on using an amp - you're out. Guitar players are a dime a dozen, we'll replace you quite easily. In fact, it would be so easy to replace you, that it would become hard. Not because you are special, but because we would need to decide which of the 100 'perfect' applicants to replace you with. THAT is the hard part. Not lack of choices, but too many choices.
2. an amp is not going to give you the variety you get from a modeler.
so, if you can get away with "one sound", then it makes no difference what you use.
Now, you see, that was the answer to the question. But as to the solution to the problem that caused the question -
This has been discussed/debated ad nauseam. (not always be professionals or even "professionals")
And, while it is true that every system and venue is different and you will never truly sound the same going from one to the other - it simply isn't true. A 'flat' system (such as a PA or FRFR) is a flat system. You can't get any flatter than flat. You are either flat or you are not.
So, then, the question is - what is different between your headphones (IEM is nothing more than a fancy word for really expensive headphones) at home and your headphones at the office. Because something somewhere is changing something.
Could it be a phase issue. - fix via eq
Could it be a hearing issue - fixed by standing somewhere else
Could it be a person issue - amazing how a sound man loses his ability to mix sounds when you take the same wire that would be plugged into a mic in front of an amp and you plug it into a box that simulates a mic in front of an amp. I mean, who ever would have thought that the mic could Jedi Mind Trick someone like that.
Could it be a space issue, where it sounds different because you aren't in the same small room with sound bouncing off the walls and floors - probably not, if you are using headphones.
I say NO. You don't need to switch to a physical amp if you are getting good tone out of your device.
But, assuming you've done everything right on your end, you do need to slap some sense into the sound men. There is no reason why they shouldn't be able to mix you.
And considering the bad sounds (from physical amps) that they can mix into good sounding amps, there is simply no excuse why they can't fix it on their end.