The problem is, Ish, that she married a person and a job. She was a hit with one and not the other - and her personality could not deal with that.
People that do well in the role realize they have a job and a relationship and that those are two very different things. They have to be dealt with on separate terms.
Can Cressida do that? Heck, can Harry do that? I don't think we know that yet.
I'm going to try to approach this without getting too specific into Diana, because I don't want to end up off topic.
I agree, women marrying into the BRF (or really any RF) have to realize that they're marrying both a job and a man. Essentially they have to be right for the job while also be able to get along with and (hopefully) be a good friend to the man. In the 21st century we're also seeing more of an emphasis placed on love matches (previously while some royals did love who they married that was more of an added bonus).
One of the things that the BRF has proven is that it is really great at finding prospective brides who would be good for the job. Queen Alexandra, Queen Mary, the Queen Mother, and Diana were all great at the job. They've also been really good about finding prospective brides who understand the demands of their position and the role of their relationship. The best example, in my opinion, is Alexandra, who was essentially a good friend to her Bertie and willing to accept his flaws and mistresses to a remarkable degree. Most of the individuals who didn't marry into the family with love, like Alexandra, knew what they were getting into and were accepting of that. The flaw in the Charles/Diana relationship was that she didn't seem to know what she was getting into in the first place, and when she figured it out she wasn't accepting of it (not really faulting her there though). In the end, when put into a situation similar to what many royal wives had dealt with before her, Diana couldn't handle it no matter how good she was at the job.
What's this mean for Harry? I do think he's able to handle the basic job. Maybe not with all the grace of his mother or grandmother, but it's something he's been raised to do and I think do he can do it. I also think he knows, perhaps better than his father once did, the importance of stressing both the relationship and the job to any perspective bride. We've seen that more with Sophie, Catherine, and Camilla, and I think we can expect to see it with the future Princess Harry.
I do think that's why his relationship with Chelsy didn't work - not because they weren't in love but because she wasn't right for the job. I don't know if he and Cressida have much of a future, because I don't know if they have that relationship yet or if she's right for the job. I suspect that Harry's trying to figure out both right now himself.