I think that many of these work well, and it depends on what suits you. My favourite moussaka recipe (from a Greek Cypriot) tops with a very thick bechamel, and NO CHEESE OR EGG!!! (her emphasis!)
FYI, the bechamel, for 4 portions, is made with 500ml milk, warmed with spices (peppercorns, parsley stalks, a garlic clove or bit of onion, and a cinnamon stick). It is then made up with 50g butter and 50g flour.
But rather like cassoulet, paella, our hot-pots, pies & pasties, I'm sure that every area, and every cook, had their own version, that they adapted when stocks of certain ingredients were low (in a subsistence economy, I can't see precious eggs being added to an already rich dish)