Eddie Vedder
Scott Stapp
Gavin Rossdale
Scooter Ward
Scott Weiland
Aaron Lewis
Marcus Mumford
Chris Cornell
Brad Roberts
The guy from Seether
Sully Erna to a lesser extent
All of those guys have clearly attempted to copy Anderson's vocal style. So does that make him the most influential rock singer ever?
Wow, I don't see that at all. Ian Anderson's voice is very nasal, and one of his aims in his music was precisely NOT to sing in an American accent as so many of his British Invasion compatriots did, but to use his natural voice and accent. But I don't know many of the references you put out there.
One artist who I think sings very similar and in a folk, but different tradition to Ian Anderson was Cat Stevens. He had a kind of throaty nasal sound to his singing too.
Anderson's voice, to my ears, always sounded like some weird British/American South hybrid to me.
I can definetely hear some similarities between Cat Stevens' and Anderson's voices. Eddie Vedder especially sounds like Anderson in ways that Stevens doesn't, and most if not all those other singers I listed came after him and seem like they may have been trying to emulate or at least invoke Vedder and/or Anderson.
Eddie Vedder has a very powerful voice. To me, Ian's voice has never been super powerful, especially in concert. He has amazing control and gets exactly what he wants in the studio though. I've never liked the live sound of Ian's voice. I used to go to the concerts because they would play really cool instrumental jams. Original made up stuff or classical music rearranged, like Bach or Beethoven. Back when they used to smile and look like they were having fun on stage .. which is not the case any more.