Not to derail the thread into talking about Marvel, but I think that many of their movies have appropriate balances of comedy and drama. Black Panther had the perfect tone. Some comedy, but overall pretty serious. Winter Soldier and Civil War actually took their stories very seriously. I think (with the exception of Ragnarok, which did take the comedy way too far in my opinion), the Marvel movies chose a tone that works for the story/character they are working with for each film/project. Spider-Man: Homecoming was a teen comedy/drama, Winter Soldier and Civil War were political thrillers, Ant Man was a comedy, Daredevil is a serious crime drama, etc.
Plus, I think the problem with DC's movies has been more based around the fact that the stories are convoluted and the characters are inconsistent more than the tone being problematic. Justice League actually had the tone I would want from a JL film, and most of the characters were written pretty much how I would expect them to be.