Death isn't the only way a reserve leader takes over. Cal retired (I'm guessing he was the Fire leader after Charlotte's mother, and Charlotte after him). As far as leaders "currently not taking battles", well you first have to remember that Noel and Charlotte are somewhat of an exception. In the new phone like things that replaced Jim Guy (or whatever you want to call him), game!Ame said she wasn't aware that Dr. Connal wasn't allowing battles, and that it "wasn't part of the deal".
As far as the rest goes, I'm gonna have to agree with GenOneRaisedGenY, game!Ame has alot more on her plate than making sure all the leaders are available for battles at any given time. However, I believe in Episode 15, Florinia said that the system is being revised (in-universe, of course).