This is probably because it's not economical to recycle lithium ion batteries, certainly not for the lithium itself. Lithium is an extremely abundant element. If this ever stopped being the case, or if there are other battery components that were scarce enough to make batteries economical to recycle, we'd start doing that.

There's no virtue in recycling equipment for recycling's sake alone, we do it in exactly the situations where some raw material in the equipment is expensive enough to justify the cost of the recycling process.

Your argument can't be both that "the batteries are recyclable" and "well duh no one does it because it doesn't make any money."