This is a tuning method I picked up way too late. I was always too reliant on tuners and was finding that even after tuning up, the guitar just didn't sound together.
Doing it this way is the way to ensure all the strings are on the same wavelength, and I think it's great for ear training and fine-tuning adjustments, and later on some note recognition.
I also see a lot of new guitarists tuning down or up just to hit the note on the tuner. I was always taught if you needed to flatten the note to go past the target and then come back up to it so that the string binds tighter and it stays on pitch. I also see a lot of guitarists who settle on "close enough" to the tuned note, but 1 note on the guitar might be close and a little flat, and 1 might be close but a little sharp, which creates a larger gap in context. If I have to sacrifice, I try to go just slightly sharp on everything.