Printing Cards From "New" Jira

I don't know if there is a free solution for the problem, which also works for a single click (meaning that you don't pay with your time instead of your money).

You can use our app to produce a PDF like this (more samples) with one click from an arbitrary list of issues, which can be printed and then cut to physical cards:

You can customize the cards (add or remove fields, change the layout, remove the QR code, etc.) and even the paper. If you have a card printer, then you can print each issue to a separate page, so there is no need to cut anything...

(Discl. it is a paid and supported app developed by our team. Free for 10 users.)

A plugin to make this easier is probably what's required.  When I've needed to do this myself,  I've exported to .xls or .csv and then used my 20+ year old mail-merge skills in MS Word. :)  It's a bit of a faff to set it up initially, but the process for subsequent print runs, is a lot easier.