The problem with modern insulation is that it's often made out of fiberglass or something else that doesn't tolerate moisture very well. Such insulation materials require an intact vapor barrier on the warm side of them to keep water vapor from reaching the insulation and condensing when it reaches dew point temperature as it cools on its way through the walls. Old houses have insulation materials that can withstand moisture much better than something like fiberglass can because they are hygroscopic, which means the water molecules are adsorbed by them without the water becoming liquid thanks to their chemical properties and very large surface area per mass. Water molecules attach to the surface of such materials without coalescing into tiny droplets of water. So long as there is no liquid water, it's impossible for microbial growths to occur.

Vapor barriers on the warm side of the insulation do absolutely no harm under any circumstances, though. It's always better for the insulation materials to stay as dry as possible because there are limits to their ability to adsorb water. For example, our house was built in the early 2000s and it has wood fibre insulation, which is hygroscopic and also very good an insulation material. Yet, the building code requires that the vapor permeability (ability to let something through) of the drywalls be five times less than the outer parts of the walls. This is because the drying of the cold side of the insulation layer is essential. This ensured using a vapor barrier paper that fulfills the 5:1 permeability ratio requirement I mentioned above.

Both modern and traditional wall structures are based on sound physics. The main difference is the use of non-water molecule adsorbing and cheaper non-wood based insulating materials in modern houses that require high-quality vapor barriers.

What I find dubious is the purism that insist on "breathing" wall structures, that is, wall structures that should retain moisture and return it to the indoor air. That makes no sense. During the winter when indoor air is relatively dry it's much better for the moisture in indoor air to be kept indoors for comfort and to be ventilated out in a controlled fashion rather than to be allowed to be removed by diffusion through the walls. There virtually is no chance of moisture damage from water vapor inside a house even during the heating season because even modern living with indoor bathrooms and cooking tends not to produce enough water vapor to raise the relative humidity of indoor spaces anywhere near 100% except for short periods of time in bathrooms, which should always be properly ventilated, by the way.

An ideal wooden house has proper vapor barriers but wood fibre insulation to maximize insulation and save money as well as to be more tolerant of moisture load.