It doesn't matter whether hierarchy is good or bad, because it's as unavoidable as gravity.
You do still have two options. 1: Honourable forthright explicit hierarchy. 2: Sneaky monkey ook ook hierarchy. Sophists are not unaware of this restriction.
That said, some explicit hierarchies are self-defeating. "Italian Officers expected that, even in the field, unless actually under fire, they would dine off of china, and drink wine out of crystal, all served by white gloved mess attendants." That's a signal of weakness, not strength. They are demanding like petulant children, not robust like adults. If your hierarchy needs this sort of nonsense for maintenance, it is a revolved hierarchy; it has already flipped to 2 and is likely to collapse to explicit egalitarianism soon. These idiots are not in charge. (To avoid misunderstanding: there's a big difference between can and must. The peasants, clearly, can't. Whether they must or not.)
If you have genuine higher status, you don't need to pay any attention to signalling. It's actively difficult to hide. (Narcissism BTFO.) You shouldn't eat in the private's mess, but not because it will make you low status. You shouldn't eat in the private's mess because you will unavoidably make the privates feel bad about themselves by comparison and make the conversation inherently awkward. Plus they're kind of dumb and you have to patronize them. It's simply ineffective. In other words, in extremis, it's not a real problem to eat in the private's mess. It's costly but it's hardly unaffordable.
It's important to repeat these things, because the outside world will continually repeat their lies.