I don't think that way of constructing consent is really viable if you want to maintain a clear definition of rape.
There are all kinds of things someone could lie about in order to make them seem like an attractive sexual partner. Who else they have had sex with, marital status, how much money they have, etc.
The tendency to want to make these very general, flat definitions around sexual crimes isn't helpful, I don't think.
I would compare to how we think about theft. There is a difference between mugging someone, extortion, burglary, mugging, financial abuse, for example. All can be very serious, but we do differentiate between someone who embezzles money from an employer, and someone who threatens someone with a weapon to mug them, maybe even using direct violence. Even when the amount of money is larger in the former instance.
There is even stuff we recognize as immoral but not necessarily a crime, like hard sells to people who are a little vulnerable, or some kinds of telemarketing.