As someone who loves Ginny, don't you think Ginny deserves better than Harry?
No. To be fair, though, it'll forever be a better argument against hinny than the idea that Harry deserves better than Ginny.
The only actual "problem"
The thing is, the story ends with Harry having a giant debt towards Ginny, but that part about Harry wanting to talk with Ginny for hours, days, and years, is meant to make the reader understand that the debt will be extinguished.
The reason why the reunion between Harry and Ginny can't be shown is this: the second Harry goes back to Ginny he's not moving from there but the plot of the Chosen One needs to end with Ron and Hermione, they are the Chosen One's companions.
That dichotomy that exists in HBP between the Chosen One and Harry continues in DH, and as in HBP, Ginny is associated with Harry. Every time you see Harry Potter thinking about Ginny in DH, it is Harry prevailing over the Chosen One.
Ginny is the most important person to Harry, this is shown a billion of times in the last two books but to the Chosen One? Well, not only she is not his companion, she is a bit of a pain in the ass. She is a living representation of everything that exists outside of killing Voldemort. He is not supposed to think about her.
It's what Ron doesn't understand when he accuses Harry of not caring about Ginny. That accusation shakes Harry so much that he starts wishing not that Ginny is thinking of him but that she knows he is thinking of her. You could also see that as the moment Harry starts acknowledging the existence of that debt we were talking about.
That said, the actual very last scene of the series is between Harry and Ginny and it's a very explicit parallel to the first time Harry saw Ginny in 1991. Again, with the last chapter, we see the end of the Chosen One story, but Harry's one? That ends in the Epilogue with Ginny. She is never meant to be his companion during the war, but his future. As I said many times before, Ginny has her own story, what kind of equal to Harry could she ever be if she was dragged into the role of his assistant? Not that it would actually work with Ginny's personality, you'd need to re-title the books.
That whole matter aside, Harry is great for Ginny.
He shares her love for Quidditch, and for both of them it's a representation of freedom, they have the same values, priorities the same things, and have the same way of processing their emotions. Ginny, who hates to be vulnerable because it always comes at a cost for her, finds in Harry someone that since he was twelve never made her pay for that vulnerability.
Ginny finds in Harry not only someone she can make laugh or that can make her laugh but someone she can build jokes with, a teammate. It's also important to note that humour is part of their communication style, they use it also in highly emotional conversations. It's not that obvious to find someone you share that with.
Harry has the power of grounding and calming Ginny, something that very clearly no one else can do.
He displays a willingness to show himself vulnerable that he never really offers anyone else (with maybe the exception of Sirius on some level).
His overprotectiveness balances out her recklessness. Harry's overprotectiveness would suffocate anyone that doesn't have Ginny's hatred for being protected, and in the same way, Ginny's excessive need of being independent would stray her away from anyone who can't contrast her on that.
He seeks light and joy and is kind after all the darkness he is gone through which is the same thing Ginny does. Their connection to Voldemort is a shared experience for sure but it's not what makes them compatible. It's the fact that they respond in the same way to it. It's crazy how people take that for granted. And on that note, they have the same emotional resilience.
And also, a very underappreciated thing, Harry breaks out of his bubble of self-centrism for her and actually observes someone else's life. Not because there's some mystery to solve but because it's Ginny and observing her surrounded by friends, learning about how she influences other people's lives, the relationships with her brothers, is worth it.
I think believing after a first read of the books that Ginny deserves better is a reasonable perception but overall an incorrect one.