"Personally, I can’t imagine why someone would want to cut strings prior to fitting"

Ray, for a little bit of enlightenment I recommend you watch this video by Taylor Guitars and Elixir Strings, and all will be revealed.

In 61 years of playing the guitar (amateur and semi-pro) I've used every restringing method known to man and beast, including your method, and I used to heap scorn and ridicule on what's now become known as 'The Taylor Method' until I actually tried it! I found it the easiest, most straightforward method of all, and with a much reduced risk of scratches/other damage to the headstock, and far less chance of blood-letting/eye-poking.

Disclaimer: I'm not a Taylor guitar fan, never owned a Taylor or even been tempted to own one, I'm strictly a Lowden/Brook/Martin man. But the 'Taylor Method' is the only method of restringing I use now.