I agree with your two problems, but the problem with your alternative and so many others presented here is that it doesn't so strongly speak to the distinction which EY means to draw, between wanting to be seen to have followed the forms for maximising expected utility and actually seeking to maximise expected utility.

Also, of course, one who at each moment makes the decision that maximises expected future utility defects against Clippy in both Prisoner's Dilemma and Parfit's Hitchhiker scenarios, and arguably two-boxes against Omega, and by EY's definition that counts as "not winning" because of the negative consequences of Clippy/Omega knowing that that's what we do.