If I'm correct, I think "plate sizes" is a set of measurements that comes from the world of engraving (copper plate &c). Daguerre used these sizes because that's what was readily available then, and the daguerreotype is a silvered copper plate.
I would suspect that part of the reason for the demise of plate size would be the standardization of tooling in the industry. Suppose your machinery is calibrated using whole multiples, and your raw stock is cut accordingly, then you don't want to have waste from cutting down into imperfect fractions the raw stock.
Think of paper, for example. In North America, the Letter and Legal sizes are vestigal sizes, and not proportional to each other. Their origin is somewhat obscure, but the force of habit (and Ronald Reagan...) made them stick. In comparison, the ISO standard (A-sizes) was built from the ground up for minimal waste and homothetic proportions. A single sheet of A0 can contain all the other sizes. What's more, all the sheets have the same aspect ratio, so it works great for photocopies. By folding an A4 sheet in two, you get two A5 sheets. (cf.
http://en.wikipedia.org/wiki/Paper_size)
In the context of the ISO standard paper sizes, North American Letter and Legal sizes fall between the cracks of optimal breakdown. If a manufacturer were to use reams of paper calibrated for A-sizes, he would lose money cutting it down to Letter and Legal sizes, because of the leftovers.
Applying the same reasoning for film sizes would make sense. I hope someone has historical data about that, because I'm speculating here!