> Is recycling even economical today?
Very much so. I suggest watching the following video to see where we are at. [1]
> Won't it become less so as new batteries become cheaper?
Recycling will be the key to making batteries even cheaper. Getting already refined iron, nickel, and other chemicals will be far cheaper than trying to mine these materials fresh.
Very similar to how pretty much all lead acid batteries are recycled. Mining new lead is a lot more expensive than reusing old lead.
Recycling isn't always economical (see paper and plastic) but in the case of batteries, it absolutely is. The biggest problem battery recycle have is there's simply not enough batteries to recycles. Demand far outstrips supply at the moment.
[1] https://www.youtube.com/watch?v=s2xrarUWVRQ