First class boarding first is absolutely the wrong way to speed up boarding. https://www.youtube.com/watch?v=oAHbLRjF0vo
The few times I flew business it wasn't separated. I felt really awkward while economy passengers were boarding and staring at me in my seat while walking down the aisle.
When I'm flying economy (most of the time) I always avoid staring at business passengers so they don't feel awkward as well.
You'd have to completely finish boarding for lower classes and then give a decent grace period for first class passengers to just show up at their leisure.
Also first class (and often business) are kinda separated so no one stares you down.
I fly premium economy sometimes and you're the first to board and sit upfront and then you have to watch everybody walking by!
It's a world of difference between premium economy and business, sigh.
Norwegian Air Shuttle had a pretty cool idea with their premium cabin. It's not crazy expensive but the seats are so much better!