I'm not sure of the numbers on that, but even if so, it's much easier to mandate the recycling of a product that has net value at the end of its life. Currently, lithium batteries do not. If you are waiting on a rising cost in raw materials to make it viable, then battery packs will become correspondingly even more expensive.

Edit: It might also be an effect, that recycling mandates had to be introduced, becase lead-handling mandates had dissuaded anyone from recycling them. Not that I'm aruging against lead-handling mandates, it's a pretty nasty material.

Even before a lot regulations around car batteries had a pretty high recycling rate. It's a lot metal to just throw away. However, even being the minority of occurrences one battery is a lot lead (a heavy metal) so it does not take very much to start being a concern.