Hmmmm, lessseeee:
1. Les Paul wasn't the inventor of the solidbody electric guitar (solidbody lap steel electric guitars had been around since 1931 [Rickenbacker's frying pan guitar], Rickenbacker, Vega, and Slingerland [yes, the drum maker - they also made guitars up until the 1940s] made small quantities of solidbody electric guitars before Les Paul made his Log guitar), he was a pioneer in solidbody electric guitar development. So, when Leo Fender's Broadcaster, that morphed via a name change (to keep Gretsch happy copyright-wise, since they had a Broadcaster line of drums) into the Telecaster (I LOVE my Tele! - they're not only good for country, but they sure do dish out the rawk! [Jimmy Paige recorded all of Led Zeppelin's first album, with a Telecaster]), showed that yes indeed Virginia, there is a market for a plank of wood, with a neck, a set of strings, and a pickup, Gibson decided in 1951/early 1952 to develope their own solidbody guitar. To help sell it, they got Les Paul to endorse it (which is kind of ironic, since Gibson very nicely ushered him out the door in 1941, when he tried convince them, to make a solidbody guitar, using th concepts he developed with his Log guitar), since he was a pretty big pop music star at the time (along with his wife Mary Ford - Les and Mary even had a popular TV show), who was well known for his guitar playing.
The Les Paul guitar was only moderately sucessful, during its initial production run from 1952-1960 (it was not a cheap guitar to buy in the 1950s), and might have been discontinued as a model sooner than it was, if it wasn't for Les Paul's endorsement. IMO, as a result of Les' endorsement, there were more Les Pauls available for bluesmen, and nascent rockers to rediscover in the 60s. The rockers and bluesmen were wowed by the Les Paul's sound, and the fact that the guitar was the one that Les Paul played, probably added additional cachet to the its appeal. When these rockers and bluesmen became successful, other musicians heard the Les Paul, and demand for the guitar skyrocketed - so much so, that Gibson took the then unprecedented step, of re-introducing the guitar into their product line in 1968, and they make it to this day. As a result, the Les Paul has become an icon of rock and (to a lesser extent) blues. Think rock & roll imagery, and typically you think of a Les Paul, and/or a Fender Stratocaster. No Les Paul today (due to it tanking [like say Gibson's first bass, the EB-1], after only being sold for a year or two, due to Les not being around to endorse it), and it can be debated that whatever would replace the Les Paul as an icon, isn't as powerful image-wise.
2. Multitrack Recording - Les Paul was a major pioneer of multi-track recording, and the sound-on-sound recording (which allows the creation lush, multi harmony soundscapes, without having to have a full blown orchestra), that is possible to do with a multi-track recorder. If he hadn't been alive in the early 50s, to expiriment with mutitrack recording on an Ampex 8-track recorder, showing what was possible (Les Paul and Mary Fords 50s hit song 'How High The Moon" was a direct result of Les' multitrack experimentation), it's possible that recorded music would have had the same kind of flat, "everybody play and sing into the microphone" sound that was prevalent in recorded music in through the 40s and early 50s, for at least another decade. In other words, backwards sounding guitar tracks, layered vocal, and guitar tracks? You'd have to wait longer for them to appear in music.