The big three is not CFOP/ZZ/Roux. The big three is CFOP/ZZ/Petrus. It was and has been for a decade.
Only recently Roux has become the second top method. So sometimes people get confused about what the big three refers to.
Roux is absolutely *not* part of the big three. It is however equal or 2nd best to CFOP depending on who you ask.
Well the idea is that if you’re equally fast at multiple methods, you can pick the best method for each scramble. But that opens up another issue—if you’re looking at multiple methods in inspection, you can’t look in-depth at anything. Like if you search for a Roux block, and a cross, and an EOline/EOcross to choose which is best, you don’t have time to look for cross+1 or the Roux/ZZ equivalents.
The way I do method neutrality is exactly doing the opposite.
My default if looking at a White(or fallback Yellow and sometimes other colour) cross. But, If I see a 1x1x2, my mind goes into method neutrality. So I scan for both Roux FB and Petrus 222, going with either that I see an easy piece first. IF there is a Full 222 in Inspection, in rare cases I can look far enough to make an X-Cross out of that.
Method neutrality doesn't work in the regard that you use it in every solve, that would indeed take up too much inspection time. You train for all methods to be fluent and roll with what you seem as best.