It is not just the used single mic and its frequency response. Your cab does not sound the same for your ears as when mic records it in 10cm. Miked cab can sound similar only when used multiple different type mics but noisy stage doesn't allow that. That's why good compromise in live is using e.g. SM57 (flat) or Beta 52 (scooped) and mixing it with DI sound.
In studio you only need clean DI and your favorite preamp sound, rest can be done afterwards (reamping, cab sim, plugins etc).
Edit: Edited a lot.
I'm alright with that. I just need the fuzz not to sound dreaful! So I think that can be achieved with a mic. I'm not sure that our desk can realistically take an extra signal to allow me to mix in the DI, but I'll have a look.
Studio, I'm not so worried. I will test it at home with a cab sim.