Then don’t feature them in behind-the-scenes coverage either and stick to rotating personnel, which doesn’t mean one couldn’t introduce brand-new characters with other functions on the ship or elsewhere (eg. an S2 captain other than Pike). But TOS also truly focused only on Kirk, Spock and McCoy (though the other characters had much greater roles) so it’s not that conservative.
The problem is you can only do that to a point while claiming in official timelines that the continuity is the same (hence the eyebrows raised on Mudd’s violent portayal), and even with a reboot the question is what is gained by using a legacy character. Is the show saying something new that entirely makes sense in context, is there a story-driven need to do that as opposed to merely using the character as a named audience hook?
Not sure why you are so obsessed with behind the scenes coverage. It sounds like that's all you watch, since the show has introduced a number of brand new characters with other functions on the ship as well. TOS focused primarily on the bridge crew, a doctor and an engineer. 3 out of the 4 follow series did the same. So continuing to follow suit is conservative. Your confusion the how's and why's of including Harry Mudd in the series further demonstrates you are more interested in the narrative around the series and franchise than what the series actually has to say about including him. I see enrichment, but then I'm all for exploring legacy characters provided they are enriched by the exploration, as that benefits the franchise as a whole..