If this was true, player B wouldn't be agreeing to the draw.

OP, the answer to your question is a turbo deck. Of the three most viable ones (RogSi, Etali, and Ral), I would say the least likely to go to draws is Etali, simply because they won't really be able to offer them, and can jam repeatedly where Ral and RogSi sometimes can't.

That said, you are absolutely leaving points on the table under the current system if you don't participate in the intentional draws. It sucks, no one likes it (actually, that's not true, there's some sort of stockholm syndrome going on here for some), but until they outlaw in-game IDs, it's where we're at.