the KEY here is, if you are using the 3K cards with no performance issue, then by all means continue to ues them..
But if you're trying to use the 3K cards, on a 1080 size to 1200 size screen, and you are experiencing performance issues, well then most likely you've hit the max of your CPU and should consider downloading the 1080p or 720p cards instaead.
Re-sizing from 3K down to 1080p needs a lot of CPU. and If you don't have it, why struggle with it..
Better to download the Clip size that Best works with your Screen / Hardware.
but to answer your question.
NO, you don't have to have a 4K screen to use the 3K clips.
even on a 768 high screen, if you've got enough CPU, yu can use the 3K clips, and let them be re-sized to fit your 768 size screen..
Will you see any significant difference between the 3K vs the 720p on the 768 screen?
I doubt it..