I'm curious as to the context of this request! The only square hardware that includes a printer is the Square Terminal, and that is a thermal printer so no ink is needed.
After that, all the other printers are third party, so there's not a lot that Square can do to help unfortunately. Since the majority of third party printers are thermal anymore, there is never any ink cartridge needed. On the impact kitchen-style printers, the ink cartridge is relatively simple to install.
Now, could Square do a running counter to say that a kitchen printer has printed xxx amount of lines and it's probably time for a ribbon replacement? Sure, but in my experience it's just easier to replace it when you can't read the printing anymore.