My bank told me the reason is the feds are capacity limited on coin decontamination. Bills they just burn and print more, but coins cost too much to re-smelt.
I cannot speak to the specific challenges in the banking industry, but from a manufacturing perspective, you can't just add a week of inventory without a ton of headache.
For most supply chains, adding a week of inventory would mean bringing on additional warehousing space and filling everything they have to the gills. I'm familiar with a factory who has a few hours of inventory on-site, and no more than ~3 days in the accompanying warehouse. They'd need about 2 more equal size warehouses to add a week of inventory.