The Les Pauls frequently turn to mud but I understand in a 3-piece the girth can be nice.
I dunno... ...I think almost the exact opposite is true. The great thing about a guitar-bass-drums format is how much sonic space is available for each instrument, and if there's too much low end on the guitar (which IMO is a characteristic flaw with modern Gibson Les Pauls that's made worse by how many guitar players use too much bass on their amps) it muddles up the mix by conflicting with the bass and the kick drum & toms. Strats (Hendrix! Robin Trower!) and Teles (Andy Summers in the Police!) work great in trios. SGs (Clapton in Cream!) too. And old Les Pauls -- the sound of early Clapton, Kossoff, ZZ Top, but those were with vintage Marshalls, by and large with the bass all the way off (or nearly so, if not live, by the engineer who recorded them) and that's a very different sound than what the guy in Rush uses.
Not that I'd know. I'm not much of a fan.