Tbh they're not that bad, and the characters that have them generally need them. Brainiacs isn't that much of a threat unless you're on a level with a background bounce, captain cold is fine tbh. I find supergirl annoying, so naturally I find her d1 annoying too. Personal issue though.
Still, once you've run the mu's against decent players a few times you'll learn what to expect and look out for and how to deal with it, without getting low profiled all the time