I see what you mean about the account of their relationship being lacking. I've always found the sisterly relationship to be the most important in this novel, but certainly there's a lot more than that.

I don't mind Austen's way of glossing over the icky love stuff. Considering the passionate and traumatic relationship that Marianne just emerged from, I think it's important that some time pass before she starts to think of marrying someone else. It is enough I think to understand her passionate nature and that she wouldn't marry someone she didn't care about. If Colonel Brandon came proposing right after Mrs. Dashwood said she approved, it would be too soon and seem a bit pushy on Brandon's part. We can reflect on his affection for Marianne throughout the whole story and see that it was never obtrusive. He waited for her to grow up a little more. Since it was a year and a half since Elinor and Edward's engagment that she marries Brandon, perhaps the story was good to wrap up how it did. If it continued and showed more of their courtship, and then showed her marrying him with only strong esteem and lively friendship, people might find that unsatisfactory. Maybe some find it unsatisfactory anyway.