The Romans weren't overthrown. They collasped inwardly and merged with the native peoples.

Ancient and medieval weaponry choices were ultimately governed as much by economic factors as by culture or personal preference or abstract comparisons of technological efficiency. Organized warfare requires organized sources of supply for weapons. Surplus wealth would permit the purchase of some weapons and armor made elsewhere and imported, but the primary source of the largest proportion of any army's war tools had to come from their own production centers. In parts of the world where there were plenty of metalworking artisans who were competent to make mail garments, mail was no doubt commonly used in preference to items that were made elsewhere and purchased. Where the local shops were better at producing a coat of plates than a mail hauberk, the coat of plates was probably what the locals wore.

It is seldom a matter of deciding which weaponry is technically superior, in the abstract, and then reworking your economy to produce that weaponry. If you have a ready source of supply of a reliable weapon, you use that weapon rather than looking for a replacement that might be more versatile. Tactics generally change to make use of the available weapons, more than vice versa. If you want your entire army to use similar tactics, they will need to be equipped with similar weapons, thus limiting your choices of supply. So the shifting over time from one preferred protective gear, from mail to coats of plates to solid breastplates and back again, says as much about the economies of the combatants as it does about their cultures and military tactics.

Another relevant factor in the development towards more plate is the amount of steel vs. iron that can be produced and the size of pieces that can be made. As explained here, the amount of ore that was converted to steel and the size of a bloom both increased with time.

Since mail can very successfully (and perhaps better) made with soft iron, it can be made with greater economic ease than plate which required larger, purer blooms of steel.

Another advantage of mail is durability, a relative amount of comfort, and ease of maintenance.

Unlike lamelar, where the cords have to be replaced occationally, due to wear and tear, a mail shirt merely has to be oiled and used to keep it in working order.
It's also easier to wear for extended periods, and simpler to transport.