You can tie the same knots without cutting the string. Just grab the two sides, pull them snug, then tie the knot. The fact that the “free ends” are connected at a distance doesn’t prevent the knot from holding like usual.

The advantage of the continuous loop is that it can’t end up inside the waistband during laundry.

Once I had a pair of the continuous loop sweats, I turned all my sweats into the same. My drawstrings always seem to end up getting retracted into the pants.