FormerlyHemlock
Hero
It is not, however, incompatible with the Standard Game. HD, Second Wind, and overnight healing are already contrary to the idea that hps represent serious wounds, and that restoring those hps them must include the wounds disappearing. No wound heals with a little rest and untrained first aid in an hour, no nearly-fatal wound heals on its own in 1d4+1 hours, and no remotely serious wound disappears while you sleep.
It's a fantasy game, with fantasy physics, fantasy astronomy, and fantasy biology. All these things that you say are impossible are exactly how it happens at my table, and the Standard Game says that is just fine. You don't get to tell me that that's not allowed in 5E, because clearly it is.