Can donors store their card details on dashboard?
It is possible to achieve this with a modern token based payment processor like the iATS Payments extension which we wrote the code for. One example of such card-on-file feature already exist:

A process button in the recurring series screen -> this lets admins charge a one time amount to a card-on-file. This could be for e.g. a catch up transaction, an additional year end donation (phone bank calls donor and gets ok to use the card on file) or for a purchase at a silent auction (where to speed up checkout credit cards or bank accounts (ACH EFT or e-cheque) were processed and tokenized ahead of the event).

So a use my card on file does not yet exist for a donor to select as a payment method - it’s definitively possible to put that together.