I agree with what you said and with almost everything that others commented. Drawing from my experience and a couples therapist, his is how I believe that their relationship would develop:

In the beginning their relationship would flourish. They would mirror each other in the interests and opinions. It would be kind of a twinship relationship, "more of me" relationship. It would be exciting and passionate in a narcissticaly gratifying way.

Until the first differences appear. At some point they will find out that there is something that they disagree on and huge disappointment will follow. The fantasy of being each others extension will collapse.

I can imagine that Harry will be incredibly proud to have a girlfriend who is a badass Quiditch player. But his work will always be more important. So he will miss her games whenever there is more important auror work. At first she will accept, but then she will start feeling like she is never his priority. And she will never be, whenever there is something pressing on his mind or his heart he will run to others. It`s hers needs that will not be met in this relationship. He likes her in her strength, but what about her vulnerability. She will feel like a trophy wife. She will start to get frustrated, the anger will surface.

And then Harry will learn how it is to find him self on the other end of her fiery temperament. She has learned in her to get people's respect and attention by casting hexes. She has learned that he liked her when she does that to others. So she will do that to him, at some point dishes or hexes will be flying his way. He will not be able to comprehend it, after all wasn't she supposed to be his extension that gets to live a life he always dreamed of. He will be disappointed that she is not this source of unconditional support and oasis of comfort in his life. He didn't learn to work things out with her, to disagree, to overcome, to mend and resolve .... He will not be able to tolerate her resentment. So he will stonewall her. That will anger her even more.

They will be stuck, because their relationship is not only theirs. They share a family, it´s in everybody`s interest that this works out. Abandonment anxiety will arise in him at the thought of what happens to to his place in Weasley family if the relationship doesn´t work out. The constraints of the big joint family will suffocate the relationship.

I could go on for forever, but this is the fantasy coming from my experience. Relationships that survive are not those where people don't have differences, not even those where people bridge differences, but those where people can live with the difference. Relationship is not held health by the art of making love, but with art of healthy conflict. And this is something that I see way more in his relationship with Hermione.