I have seen or heard of such romances. I even know a couple of stories of, in this case, young women who had had stuff like their parents divorce, absentee father, bullying in the course of their teenage years and then found a loving partner , a few years older(we're talking early twenties vs his late twenties or mid 20s with early/mid 30s in these two cases), who made a lot of difference in their lives by providing that positive ,real proof that what they experienced isn't the only way things are, which in turn also opened them up to the world and to that necessary vulnerability you need to have in order to give and accept love and intimacy, both physical and emotional.

So yeah, the stuff from the movies exists and even from the history of the past hundred years, I know of cases where there was an evident strong love going on.

The thing is that the movies don't show the entire life of a person and their entire relationship, usually. A good ,loving, successful relationship isn't one that lasts a lifetime but one that is good while the feelings are there and both parties want to be in it, one that is good while it lasts and ends decently, not in major scandals/fights/abuse of some kind.

Movies perhaps leave us with the idea that real, passionate, successful love is the fairytale one that is never ending, that has no problems, precisely cause it is built that way in the movie/story or because of the story showing only a part of the relationship, the beginning and maybe the middle but not how it ends(with the death of one of the partners in old age or break up at some point in its future).

Also, in movies most of the strong, "beautiful" love stories are between people who are over average in looks, even those somehow presented to not be so in the actual movie, are in fact quite attractive.
I don't think that love and attraction are all about looks. The relationship itself, once it began forming, is probably less and less about the looks and more about compatibility, personality, the way the partners manage to nurture the relationship and show eachother respect.
However, the more physically attractive and charming you are at first glance, probably matters a lot because the first impression matters a lot and can either broaden your potential partner options or lessen your options. When you are young or middle aged (particularly as a man) and physically attractive or sexy in some way that comes out on first glance, there are probably more chances to stir passion in more people, some of them equally attractive and alluring and from diverse backgrounds, so there is more potential for that strong, passionate, heated romance thing.

Another thing related to stereotypical physical beauty is that it sadly influences how people perceive your personality traits and behavior. Let's take lack of self esteem/shyness/social anxiety ,for ex. Say you have a conventionally good looking woman/man who suffers from one or more of these and a not conventionally good looking woman/man who suffers from exactly the same thing. Let's say both are influenced in a similar manner and are similar in intelligence, interests, both with a good heart and lots to offer. In the conventionally attractive, shyness, lack of self esteem or confidence ,even depression ,can actually turn into cute quirks ,make them actually more approachable, cuter and more "human". In an unconventionally good looking person, these same traits are deemed as turn off's. It is proven, sadly, that conventionally good looking people have an advantage in how they are perceived because the human brain sadly tends to put an equal sign between what is regarded as physical beauty and the inner qualities one possesses.

So yes, if you're conventionally good looking, even such stories as often portrayed in movies, of a tormented, damaged soul finding the extra strength and comfort needed to really put themselves back together/having someone fall in love with them and see beyond the damaged part into their true potential, are possible and happen to people but I suspect they happen more to people who are good looking enough and/or have some particular thing about them that is charming on first glance/before knowing them more deeply, that makes them sexier, more alluring. It can happen to anyone, certainly, but...

No one ever even showed any interest in me personally and for me love was always a one sided ,painful and quite dehumanizing/invalidating thing, but it does happen, it just doesn't happen to me.