It depends on 1. the physical quality of the house system, and B. the audio quality of the settings on said house system. Both can vary considerably with every ... uh, ... house. And then there are audience qualities, both physical and audio, to consider; another wide ranging variable. It's very important to narrow the variables to get a concise result.

See A. above. Yes, it certainly can, and at least sometimes does. But, no, it often doesn't, either. But, it doesn't make sense that the tone you have carefully crafted coming from the Rumble speakers should be called noise! Not by the crafter, at least. Sounds like you prefer the headphone sound, which can be harder to replicate in an open air environment.
Oops! I must have misunderstood. So, you prefer a bad headset?!? Well, the R500c does have a cab sim in the headphone circuit, per
the block diagram. But I believe it is intended to enhance or improve the headphone sound. To clarify, are you saying that the
losses you hear in the headphone sound, which you don't like, is in contrast to the "noise" coming from the Rumble speakers? I'm so confused.

Originally, amps were mic'd because there was no other way to get a strong, clean amp signal into an FOH or recording device. But, being acoustically sensitive, several such microphones in a live band performance presented certain challenges, including feedback, crosstalk and balance. The advent of XLR Outs on modern amps, and mixing boards, helped relieve many of these challenges and to reinforce, and/or record, much cleaner signals.
However, like many innovations, not everyone celebrates using the XLR Out on an amp, instead touting the old school method of mic'ing, even these days. It's somewhat like exclusively accepting only tubes, or only certain
types of tubes, in deference to all solid state in amps and other devices. Like much else in music, it's very subjective as to "what's best" versus what's practical/easier/expedient.
Well, that's my $0.02. I hope it helps.
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