A surprising amount of developers have their own side projects. These should be encouraged by employers because a) most of these projects don't go anywhere and so the likelihood of you loosing a staff member to their hobbies is low, and b) because employees often explore new technologies and educate themselves when doing these things. It means your employee loves what they do enough to keep doing it in their spare ti…
I mean, these ideas are nice... in theory. But to play devil's advocate: a) Statistics? b) Can an argument not be made that with programming/developing/designing at work AND at home, burnout is more likely? Or that less overall effort will be spent on work related things?
As far as answering your questions, a) I don't have any statistics but I know a lot of people with side projects and they all still have day jobs, so it's very anecdotal. b) You could make that case, but I'd say (once again without evidence to back it up) that if burnout occurs it's going to be the personal project that is cut rather than the job that pays the bills.