Many people want them because they think they will get a docile, naturally bombproof personality from the draft blood. In my experience, it doesn't usually work out that way - they range in hotness and spookiness just as much as any other breed or cross does.
Then you've got folks who are looking for a mount to carry a heavier rider and believe that, because drafts are big and thick boned, they must be able to carry a lot of weight. Almost never the case, but again, way too many people don't understand what to look for in a horse's conformation to assess its weight bearing capacity.
The third and I think most popular (at least in my area) category is the "poor man's warmblood." As you can tell from my username, I own a draft cross, and I do dressage with her. She's never going to be confused for Bretina, but she's got the substantial look (at least she does when she's not a big fat hippo) and big stride that is generally preferred for the dressage ring. She's never going to be an FEI level horse, but then again, I'm also never going to be an FEI level rider and I did not want to pay huge money for a horse with more potential than I would ever be able to use. Instead, I paid a reasonable sum for a horse who is athletic enough to be competitive and fit in at the lower levels of dressage.
A well thought out, carefully bred draft cross does not have to have a huge shoulder and no hindquarter -- there are breeders out there, particularly with the percheron x TB cross, who are producing lovely, balanced animals.
I should add that the fox hunting set loves draft crosses, but that is well outside my area of expertise/experience, so I can't speak too much about what they're looking for in their mounts.