When I was a kid starting out on guitar, I would always struggle to play something NOT cliched in guitar stores while the "audience" was listening. I don't think my local store had a "No Stairway to Heaven" or "No Enter Sand Man" or "Eruption" sign, but it was understood.

And by the time I was starting to shred, a guy named Cobain came along and ruined everything.
My musical vocabulary is much wider now, and I can improv for a very long time without resorting to playing hit songs/riffs, so sometimes as a challenge, I'll record improv sessions just with one guitar (although quad-tracked on the deck) playing something that goes somewhere/anywhere, a different guitar every time. Parts can be like a concert solo spot, and others just exploring chords and moods or playing with various effects.
I must admit, I love listening back to them just to hear the tones and where the playing went (if anywhere), and sometimes get song ideas from them. I sometimes do this with backing track instrumental songs also (me live on all instruments). Are they indulgent? You bet. Is it fun? Of course.
Some of my favorite platforms for extended improv:
Hendrix Band of Gypsys - Who Knows (I take this WAY out from where it started)
Iron Butterfly - In-a-Gadda-you know the rest

(this song was made for improv---and octave pedals!)
Goblin - Profundo Rosso (Deep Red - theme to obscure '70s Horror Movie)
Dream Theater - Erotomania (my far less disciplined, but more aggressive, perhaps drunken

, but still shredderiffic version---one take only!)
Grip, Inc. - Monsters Among Us
Racer X - Into the Night
Try it!!
