I don't think it would be easier, but I think it might be more beneficial if it worked.

I don't know how accurate that statistic really is, but my understanding is that it is a measure (accurate or not) of the number of women who say they had sex in college without consenting to it. The 20% figure is credible to me, taken as measured in that way, and might be accurate, even though I would also not be surprised if the true figure is only 10%.

I would guess, however, that the following situation makes at least some contribution to that situation. A man and a woman have sex. Neither of them mention it explicitly. No one says, "do you want to have sex?" or anything like that. But both of them make positive behavioral contributions, and a reasonable person, judging from the behavior alone, would assume that both are consenting.

Then, the woman feels bad afterwards. This surely does happen in real life, for many reasons. Now as Katja Grace mentioned in a recent post, frequently we do not know our own desires directly, but infer them from signs. So it is perfectly possible for the woman in this situation to reason, "look, I feel bad about this, and although I was cooperating physically, I never actually said I wanted it. So I likely did not give real consent."

You could say that we could repair this situation by requiring that people actually mention it and say yes.

That would repair the situation, in the sense that the woman would no longer be able to complain that she had sex without consenting. But notice that when she felt bad, that probably had little to do with whether or not she explicitly said yes: she could feel bad even if she did. And the yes-means-yes policy would do nothing to fix this.