Traditional woodenware was painted with thin, economical paint. Basically "whitewash" (though not lime based).
Hobbyists have taken to creating jewel boxes with heavy layers of paint, or alternatively coating everything with a layer of wax.
I think the old cheap farmers approach is better. It protects the wood from sun and drying, but is porous enough to let the moisture wick out of the hive.
There have been discussions here on UV resistant stains and varnishes, which the proponents claim are better than latex paints. I can see how a penetrating exterior stain would emulate the old farmer's whitewashed woodenware. I don't have a problem with a single or double coat of latex on my boxes. Left uncovered the redwood fence boards I use for mediums dries and warps or splits from the endgrain. Painted wood is much more stable and longer-lasting. Pine wood boxes definitively need paint (or deck stain) protection. I cannot endorse the various copper and anti-fungals added.
The photo's of the various wax dipping efforts I've seen are downright scarey to me. 100 lbs of melted wax over an open flame with inevitable drips and splashes is an invitation to a catastrophic flash fire. The wax-dissolved-in-volatile solvent approach seems to carry little advantage over tried and true latex.
One final thought bears repeating: Bee's DON'T care. The whole adaptive genius of the honeybee is to use its social organization to modify its nest using bee-ventilation, drying, heat production, propolis sealing and comb structure. Unlike many insects which have very specialized habitat requirements, bees are broad generalists. They accommodate themselves. Much of the obsession with particular nest styles, sizes, colors, coverings, ventilation, and opening location and dimensions are just beekeeper smoke. The bee's could care less, not one wit.