If it takes a half hour for a single round of combat then I will assert that you actually are doing D&D wrong. Players should know the rules for anything their character can do and be paying attention so they’re ready when their turn comes up. Combat and magic rules take up maybe a dozen pages in the PHB, spend an hour and read over them a few times to make those weekly games you invest two to six hours into go much smoother.
The DM should know all the rules. Like most homebrew I see, this is an overly complex “solution” that functions nothing like anything else in the game and wouldn’t be necessary if everyone involved actually learned the real rules. 5e already has an exhaustion mechanic and it works nothing like what is described. Making up new and convoluted rules to be used by people that take six minutes to move and make an attack or cast a spell is not going to accomplish anything but making your combat turns forty minutes long instead of thirty. I play in a game that includes seven PCs including two “lightly experienced” players and one complete noob. Combat rounds take maybe ten minutes, tops, because people pay attention and the DM actually learned all the real rules.