Re: Take this.....
"I believe they were originally invented to save Alex Lifeson's neck from the strain of carrying three guitars simultaneously."
Not sure about inventing guitar synths, but Alex Lifeson did invent a guitar rack/stand to allow him to switch, relatively easily, between electric and acoustic guitars during live shows - he originally sold it under 'The Omega Concern' moniker; both Lifeson and Geddy Lee made extensive use of pedal triggers in their live shows at the time (late 70s, early 80s)
That said, Rush were one of the first bands to make extensive use of synth triggers in their live shows (originally Moog Taurus/Taurus II bass pedals, then MIDI triggers and sequencers) and Neil Peart's current 'electronic kit' is basically a bunch of MIDI triggers hooked up to samplers and sequencers, so making a Rock Band-style controller sound like a guitar, Mellotron or frog-chorus isn't particularly difficult.
So I'm a Rush fan - coat's on, I'm already halfway out