I believe there's a bit more of a burden of consent than that — it's not enough to say "well they didn't say no" but it should be the case that they explicitly said yes. Getting people to be more open and informed about sex, including teaching people to actually make sure that everyone involved really wants to do the sex, can only improve the situation. It promotes more respectful relationships and gives people more confidence to say no when they really don't want to.
You're right that there are a lot of grey areas when it comes to how you'd actually define rape, but in most cases if you have to start arguing about whether something is technically rape or not it's most certainly still really scummy behaviour and should be discouraged culturally, if not legally. Badgering a person until they finally give in to your sexual demands may not fulfill some definitions of rape but it's still something you really ought not to do (this circumstance is especially dodgy because depending on the situation it can often be the case that a person feels physically or otherwise intimidated by the other and the consent given is, effectively, coerced, even if the demander is not overtly threatening). Sex isn't really something that should be done reluctantly. We also consider deliberately plying people with alcohol or other drugs in order to get them to consent to be a kind of rape — people sufficiently intoxicated or under whatever influence are considered not able to give informed consent by diminished capacity and if you take advantage of a person in that state in order to get sex, a lot of places consider that rape and even if you consider the technicality debatable it's still something that you really ought not to be doing.
I do fully agree that when it comes to the victims of rape we tend to have a kind of negative feedback loop reinforcement going, which I feel is especially dangerous in cases of child abuse. When everything tells you and everyone around you acts like you've just experienced the worst thing ever and that you should be scarred for life, you're going to end up conforming to those expectations and suffering for it. I don't mean to belittle the trauma that any victim has gone through — certainly many people are susceptible enough or simply had an experience so harrowing that they don't need any outside help to suffer in the way that they have. But likewise, I find it very likely that there are many cases out there where the stigma and and extreme response to cases of rape have hindered the recovery of victims and indeed made them feel much worse than they might otherwise have done about the whole ordeal.
Generally speaking, of course, many of these issues would be alleviating by removing our ridiculous cultural stigma against women actually having sex. If we no longer have this ritualised game of "playing hard to get" which many women participate in and men are trained to expect to have to overcome, the murkiness in the waters of informed consent is considerably cleared up. No should mean no — training people to expect that no actually means yes, eventually, or saying no because of some stupid cultural expectation that you should even if you actually want to say yes, is a significant problem in this area of our culture, and is undoubtedly responsible for many sexual assaults and rapes. It can be difficult to get someone to understand that you actually mean no if they've been trained to believe that when you say no you're just being "hard to get", especially if they're somewhat drunk or something, and especially if they're intimidating in a way that makes you fear protesting too much (which doesn't have to be deliberate at all — a big drunk guy can feel plenty threatening to people who have to deal with him even if he doesn't mean to be or realise he is). And guess what — this whole issue is a part of what people consider to be rape culture (explicitly, our culture around this issue is conducive to and results in rapes and sexual assaults). It's not all about bad jokes and yelling names at people.