I bind quilts professionally, and I never press binding in half.
Bear stated what I was going to say, but to further illustrate what we mean:
If you think about a track, as in running sports, Olympics, etc, the inside lane is shorter than the outside lane. Convert that image to the fold of binding fabric that you curve around the raw edge of a quilt. The inner layer of fabric will be shorter than the outer layer of fabric, and if you press the fold first, the inner layer will bunch up on the inside. However, if you *don't* press the fold, the fabric is then allowed to adjust naturally and will sit neater at the edge of the quilt, and you will get a nice, even, full binding. It may be only 2 or 3 threads-width worth, but believe me, it DOES make a difference.
Side benefit - you save the time and labor of skipping a step. 😁
p.s. I don't use the ladder stitch. Personal preference.