It’s safe to say there is probably no other chemical on earth as thoroughly studied as DEET. If there was a problem with it, they would have found it by now. It was invented in 1946, something like that.
Nothing else comes even close in terms of repelling Mosquitos, and it also lasts several hours. West Nile, Malaria, and probably other diseases linked to Mosquitos are far more debilitating in any case. It does damage plastics, and nylon. But I’m not made of plastic, so I’m good.
Personally, I like DDT.