Wyler,
I dispute your assertation that FC and ATC cannot mix.
I know of many who have done both. Some have gone ATC to FC some the other way.
In my own case:
over 2000 intercepts
Saw service in Bosnia Crisis and Gulf War 1.
ATC terminal and Area qualified
Different skills? Yes, but not mutually exclusive and I know many who could do both and some who could not. But then those who could not were/are not the best FCs/ATCOs anyway!