I think its funny that the type of covers they used to play live and on their albums were nowhere near TSI. Considering VR plays Floyd and Aerosmith covers, and GNR played Paul McCartney and whoever wrote KOHD (I think it's Dylan but everyone in their brother plays it), the TSI was nowhere indicative of their roots, but that's my opinion, which will get thrown to the wayside
have a lovely day!
I think the band's roots are many and varied. The roots of Axl and Izzy tend to be more Stones/Dylan oriented, and since Axl largely controlled the band, those types of songs ended up on the major albums. But I think they all have some punk influence, too (esp. Duff).