I am a HUGE fan of mutts. I think more people should embrace the mutt label with pride.
Unfortunately, mutts aren't healthier...at least not any more. Most mutts today are just a generation or two away from a purebred. If your take a Maltese with all sorts of health problems and cross it with a Bichon with all sorts of health problems you get....a very unhealthy dog. The people who are most striving to select for and test for and produce the most healthy example of a specific breed are the people who are least likely to let their carefully planned and tested dog get knocked up by the neighbor's dog by accident.
Back 100 years ago, mutts were healthier because of natural selection. Less healthy mutts died. Survival of the fittests was in play. This didn't apply to just stray mutts either but also mutts owned by the lower-middle class hunter and the lower-middle class farmer or rancher. If that dog can hunt well, catch rats well, run cattle well, the frugal farmer and hunter didn't care that it wasn't a purebred (they couldn't afford a purebred), but if it failed at those tasks, it wasn't kept for long.
Finally, hybrid vigor. Hybrid vigor is the concept that for a trait normally the offspring of two different breeds will fall between the two different breeds, (example 60 lb sheep x 100 lb sheep -> expect 80 lb adult weight for the hybrid). But there are times when the hybrid surpasses both it's parents (example 60 lb sheep x 100 lb sheep = 120 lb from the hybrid). Hybrid vigor shows up strongly when certain lines/breeds with a species mix and doesn't show up hardly at all when other species have their lines/breeds mix.
Dogs don't show hardly any hybrid vigor at all.
Additionally, until it is discovered through crossings, who can say what traits are going to benefit from hybrid vigor. Maybe it's size, maybe it's night vision, or hearing, or aggression, or shyness, or running speed. And these 'improvements' may not always equate healthier. If hybrid vigor makes the progeny even bigger than either of the parent, this can exacerbate the stress on joints, or how well those joints fit together, which may mean worse cases of hip dysplasia. Maybe whatever is causing improved night vision in a hybrid exhibiting vigor on that trait ends up being light sensitive during the day.
Anyways, when you realize that hybrid vigor can in theory show up in any trait of feature...both good and bad...maybe it's good that dogs show so little hybrid vigor.