I used to mix house for Del McCoury, Rhonda Vincent, and 3rd Tyme Out fairly frequently back in the late 90's/early 2000s when they were starting the "one mic" thing. Del McCoury Band was one of the first. It can be done well, but a decent parametric eq is pretty much mandatory because there will be two or three "hot spots" that will have to be notched out to get the gain needed while keeping some bottom, and the frequency that those spots fall upon will move depending on the room or stage-top, and even ambient temperature.
When I was doing this, "everyone" was using an Audio Technica 4033 almost without exception, and as time passed they "all" moved from one mic, to two, to three, or even more. Augmenting the bass, however, was usually the first thing they did to move away from "just one". Using monitors, especially wedges, in these situations, is almost always a really bad idea. The instruments will reflect them right back into the mic(s), and to "mix" themselves, the artists need to listen to the house (and have the chops and pipes to get it there with some meaty assertiveness).
The Choreography opportunities that brought about Reminiscences of the old days were a big part of the attraction to the artists, and frankly, they believed that it gave sound-persons fewer chances to screw up the mix. Many less experienced bands climbed on the bandwagon before they had the technique and projection to make it work, and that's really when it sounds thin and weak. Think "China-Cabinet being pushed down a flight of stairs".
Through it all, I still generally preferred close-micing individual voices and instruments... ...but you do what the boss wants.
I haven't done any mercenary audio work for a few years, but I know fewer of the big acts are using the "one-mic plus plus" method these days, and those that do have mostly moved beyond the venerable AT4033. I see a lot of Shure KSM 32 & 44s (I think) now being used by those that still want to (usually play) through a large diaphragm condenser.
I hope this makes some sense.