Oh, this will end well.

Example: I check in and get pass #1. I then check in my SO a minute later and she gets #20. She will be getting on the flight at the same time as me (since I'm usually the one lugging her carryon).

All it takes is one moron between #2 and #19 to have a problem with this and the whole system breaks down.

Most people above the age of 3 can figure out A-B-C, but that doesn't stop some people from mucking up the process or feeling the need to line up 90-120 minutes before boarding. An additional layer of complexity is not going to help.