I agree with all points - giving blanket consent up front misses the point entirely. But I've been thinking if it's possible to flip the idea on its head: Make a kind of "sex partner review escrow service". What if instead of granting consent, the app allowed you to designate a person that is allowed to 'review' you. Basically saying "I give this person the right to call me out as a sexual predator" and get the same in return. That way it'll be what they think about the encounter afterward that matters.
Reviews aren't perfect, and they won't catch someone mostly well-behaved who only occasionally sexually assaults [1]. But as it is, there are serial-perpetrators out there who get away with it, because there's no 'background check' for dating, and the only remedy is if a community around a known predator keeps trying to warn each new girl he tries to get with - which is indistinguishable from slander, and can just as well be used to ruin someone's life based on a single lie. So maybe an app could actually help with that? Make an 'official' paper trail so your sexual behavior, good or bad, is on the record. The technology could enforce various things - e.g. the review could be 'locked in' after a couple days, so you can't change it weeks later due to a bad breakup (it wouldn't even need to be published or sent to a server, a cryptographic hash would be all it takes to make it possible to verify later that the review wasn't tampered with). And by only allowing 'authorized' reviews, you avoid the possibility of brigading.
Using technology to deal with a sensitive issue, and sensitive data like this isn't easy - and doing so would require a very careful design about what is visible to whom under which circumstances (not unlike the recent contact tracing systems in iOS and Android). But I feel like a legal grey-zone like this, where the courts continuously fail to help women that have been raped, that calls for more creative solutions, even if they don't solve the problem completely. With a consent app, each person 'signs away' their right to call the other person out, but with an app like this, the opposite is true, you give weight to the other person's voice, and I think that's worth exploring.
[1] https://xkcd.com/325/