I'm aware of cab sims, but have never used one. Since my favorite cab to use hasn't been manufactured in about 40 years... I'm not sure a cab sim would really do the job, as I doubt there's a simulator for my cab.
[...apologies for a long post...]
Well, this is why many guitarists/bassists are getting really serious about their methodology with respect to cabinet simulations, and capturing impulse responses of their own cabinets, or of those that exist in studios with a really nice selection of vintage speaker cabinets. This gets discussed far less amongst bassists than it does amongst guitarists, but I'm actually pretty encouraged that the discussion about cabinet sound translating to FOH sound seems to be happening with some regularity now.
The fundamental stumbling block for those who are interested in exploring the use of custom cabinet sims (IRs) is that the devices available that allow the use of custom IRs of a higher order of quality tend to be pretty pricey. For best results of real tube amp (preamp and power amp) distortion's contribution to the tone, a load box device seems ideal, but putting that aside for the time being, there are few pieces of equipment to choose from that provide robust cabinet emulation, allowing the use of custom impulse captures. Kemper and Fractal have systems that provide the amp modeling as a key component along with cabinet simulation. Fractal Audio's AxeFxII has built-in technology that allows the user to capture their own Cabinet impulses, as well as a "tone matching" technology that is used in all sorts of creative ways to closely emulate the tone footprint of everything from acoustic guitars to stomp boxes and preamps. 2 Notes has a variety of hardware solutions like the VB101 (which includes a "load box" for speaker-less implementation) and the C.A.B. pedal (no load box).
I think the key to the dilemma of using a mic to capture "your tone" to send to FOH is to first understand what you are hearing out of your amp, and then understand exactly what your amp truly sounds like via a microphone, as
squeezer has done his best to emphasize and explain. Cabinet simulation technology is being used quite a bit now, but it is not a trivial topic. Beyond the costs associated with going this route, I see time and time again those who try to implement the technology getting frustrated, generally due to a lack of understanding what the technology is supposed to accomplish.
Ideally, you would take your rig into a pro quality studio, crank up your speaker (amp) in a "dead room" and mic it in such a way (multiple mics of various types and at different distances) that the end result is pleasing when placed in a representative full band mix (of your band, ideally, or at least something of a similar genre). The contributors to the resulting captured cabinet impulse are not only the mics, but the mic preamps used, and we all know how a really sweet mic pre can make all the difference. Again, this is an engineering task that requires great care, ears and experience. Thus it is more commonplace to use the stock cabinet impulses provided that come with "the box", and hope you can tweak something to your liking.
Let's say, then, that you've now got a .wav file captured by a software program that represents the pleasant sound of your studio-captured bass speaker that you'd like to be sent to FOH when you gig live. You'll need to load this IR into a 2 Notes or Fractal Audio product (speaker emulator), fed by a pre-amp
out signal into the speaker emulator unit, which then gets sent to FOH, while on stage you continue to monitor your bass guitar with your stage amp as you always have. If you have a load box, you can do the same, but from the power amp output of your amp. This is the state of technology today. It is still very young, but improving every day. It does work, and you don't need to take just my word for it. Major acts are utilizing it every day of the week.
Now, the whole discussion about mic'ing the bass amp or not is moot IMHO, since technology allows bassists to avoid the whole issue completely if they choose to. Whether bassists are willing to explore and dedicate time and $$$ to this solution is another story. All I can say is that my life is a helluva lot less stressful for implementing cabinet impulse technology in my bass rig. No sound tech has ever questioned the direct feed I provide, and I've never been dissatisfied with the sound that is reproduced FOH or in the monitor system. It is far superior and rewarding to any other method I have employed in my previous 25 years of performing. It's simple, elegant, and solves so many problems. But...right now it's expensive.