The two things that could have started the era was the screwjob and Stone Cold beating Michaels at 'Mania 14 for the WWF title with Mike Tyson.
The Attitude Era began after Austin won King of the Ring 1996 in my opinion. He cut the Austin 3:16 promo and set off all his success from that point on. In the fallout of the event, Austin called out Hart and that would be his first official feud as Stone Cold Steve Austin. Plus there's also what Brandon said. In a way, Hart had a big impact on the Attitude Era, though I do in a way understand how you could feel he wasn't vital to its success. Overall, I'd say he was little more than a bit player, and a pawn in Vince's grand scheme. If he wasn't on this game, I wouldn't give a damn, so I sorta agree with you, sorta don't.
That being said, if you're going to put Mankind in, you may as well put Dude Love in. Plus, it's going to look stupid to only have 3 faces of Foley, when famously, there are 4 faces of Foley.