Considering putting down cardboard between my beds. What do you think?

My beds are on the ground, not raised. It’s just grass in between them and when I mow it throws seeds in my beds and it’s so difficult to manage. Thinking about hoeing the grass out, adding a double layer of cardboard and then maybe some bark chips or straw just to hold it in place. What do you think? Do you foresee any issues? What do you have between your beds?