If my body is not flexible and the barbell doesn't go down to the ground unless I bend my knees, should I just give up on this exercise? Or should I think of it as increasing flexibility and just go down as far as I can?
I do this as dynamic stretching. It fits the purpose of exercise, and as long as I don't get injured, that's all that matters.
Doing this increases flexibility. Just do it until you go down.
There's no need to forcefully stretch your legs. You can do it with a slight bend in your knees, as it will still stimulate your hamstrings, so stretch slowly.
If you keep doing it until you can, you'll eventually improve steadily...!
I'm also just thinking of increasing my flexibility, so I'm only going down to the point where I can.