Drunk people can consent.

They can consent, but they can also not consent. And that's part of the problem.

Being drunk doesn’t make you do things you don’t want to do.

If you and a sexy person enter a room together, drunk, and that person puts a $1000 charge on your credit card, do we assume that the charge was consensual simply because you were too inebriated to coherently object?

Assuming the answer is "No", why would the standard be different for sex?