I think Cena is a rich-man's Lex Luger in a way, only with a real deep love of the business.
People didn't think Lex could work, but Lex regularly carried bad-hands to better than expected matches. When he was in the ring with a great, like Steamboat, it could be a really great match. Same deal with Cena. He took Batista, Umaga, Big Show, etc to decent matches and Shawn Micheals got a five star match out of him. He has personality, it's just not one everybody likes.
Whether you like it or not, he is legitimately one of the biggest stars in the history of the company. I guess you could argue that he wouldn't have been in a prior era, but I think he would have had the opportunity to flex different muscles in another era and you have to remember: even Undertaker was a distant, distant third or fourth during the height of the Attitude Era.
RE: Buff Bagwell. He made Roman Reigns look like Lou Thesz. He wouldn't have been a star because he's a headcase. He once had his mom call in sick to Jim Ross at Titan Tower, like four days into his WWE career (that lasted a couple weeks IIRC). A good look will get you a chance with Vince, but only a chance.