Without wanting to divert this thread in to a price point justification...the PRS SE line features a lot of very nicely made guitars that do similar things to the Les Paul for a whole lot less money. But some folks just got to have the real deal. I think that the percentage that can or are willing to afford those price points for a "Real Gibson" has shrunk substantially since the "Great Recession" that many folks have yet to recover from.
I've never played a PRS that I've liked including a $25,000 private reserve that just left me cold. PRS aside, though, there's something about a Les Paul that other dual-humbucker guitars don't deliver. I think part of the magic is what other companies try to "fix" in the Les Paul design. Les Pauls are thick and often heavy and don't have great ergonomics, and I honestly think that's just part of what makes them sound the way they do. Case in point - I have a '90s Japanese Jackson Professional Pro that is an *amazing* guitar. It is constructed like a Les Paul (mahogany base with maple top, etc.) but sounds nothing like a Les Paul. It is shaped like a Strat which makes it much more ergonomic, but it's still heavy and it freaking rocks - but it doesn't sound like a Les Paul.
If all someone is after is the general shape then any similarly shaped guitar will do. If all someone wants is a dual-humbucker guitar, then there are plenty to choose from, but to say that other guitars that are somehow similar can replace a Les Paul is to not understand the Les Paul. At least, not a good Les Paul. If you've only played crappy Les Pauls (and there's lots of those out there) then yeah - they can easily be replaced by damn-near anything, but a good Les Paul that delivers that magic timbre? You'll not easily replace that. There is definitely a diminishing returns thing going on as there is with any guitar, though.
Take it from a guy who's owned six Nightbirds, five Bluesbirds, and two many other guitars that were supposed to be "just as good". There's something about a good Les Paul that I've never found in another guitar, though the '70s lawsuit Ibanez guitars and the Ibanez Artist from the period therafter are about as close as I've personally experienced.
Now, to be fair, would the audience notice? I doubt it, but that's a whole different conversation.