Wow, this thread has me scratching my head.
Aerosmith is BY FAR the signature American Classic Rock Band. I don't even know who is close, to be honest. Lynyrd Skynrd, perhaps.
They have been successful in every decade they have been in existence.
Influence?? Really? How about every bar band for the last 40 years? They were the blueprint for every 5 piece hair metal band in the 80's. They translated to the 90's in bands like The Black Crowes.
Beatles, Stones, Zeppelin? Probably not, but I can't think of many other bands I'd put ahead of them from ANY country for success, influence, sustainability.