If that was the case, the regulation would not be needed. But before regulation a lot of car batteries would end up in land fill and are now leeching into water veins.

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.