From that perspective martial arts and self-defense training is all about pushing the power to the students. On every level. Physical fitness, of course. Technical skill, surely. But "Knowledge is power" as well, and so is awareness and understanding. If the goal is really self-defense, then the goal of instruction is to increase each and every student's power until they can not be pushed to the prey side of the predator prey dynamic. So that they are strong enough to have a choice. Always.
It's a fantasy. There is no "always." Regardless of who you are or how you train, there are levels of violence that can squash you like a bug on a windshield. There are confluences of timing and incidents and threats that can negate whatever advantages you bring to the table. there is no "safe", only safer. And that is knowledge, and in that knowledge is some power, if you can understand and use it.
It is only a fantasy of degree, though. I can't make you invincible. I can make you a harder target.
This is the way things should be... if the training is about the student. If you are not, as a student, getting stronger, smarter, faster and more aware each and every practice the training may not be about you. It might be about the style, if the emphasis is on rigid ideals of perfection. It might also be about the instructor, about he or she maintaining power. That will not serve you well.
In a vain attempt not to hurt anyone's feelings, I'm going to talk about myself here. Martially, I'm pretty competent. Ask around with people who have crossed hands with me to get an idea of what that means, since I'm too close to judge. But anyone I have trained for a year should present a serious physical threat to me. If we were to close without safety rules, I would be in serious danger.
If I can't get someone to that point in a year or at most two, I'm either 1) a shitty teacher; 2) don't understand what I know well enough to teach it or; 3) I'm holding the student back, denying them power (which they may need in the real world to keep breathing) to maintain my own power in the little bullshit world of the training hall.
That's a little different for sports-based arts. Competition allows for a very narrow but deep game. Something like chess. It's even somewhat different for traditional arts, in that the progression of teaching is set, and so there are some things that you gain in steps (necessary or not).
But if someone claims to be teaching you to fight or teaching you to defend yourself and you are helpless after 3 or five or ten years, there is something wrong. Something serious. If the tactics that so impressed you when you were young and naive still work (or, worse, you can't pull them off yourself yet)... give it some thought. If the rules get tighter as you get better, or if you are forbidden to win by any method than the ones you have been shown, it is not about empowering you. It is about something else.
Am I saying you should be as good as your instructor after two years? No. Insight, connections, integration and other things all increase with experience. I don't expect my students to be able to beat me after a year. But I would be ashamed if they could not hurt me. If they didn't have at minimum the power to make me pay for a victory. If I could still beat them easily.