Looking into it, I actually think this is a major problem. Recent foreign appointments in the championship haven't been able to bring many staff with them.
Thorup at Norwich brought one coach, that coach has been a head coach multiple times so would qualify, but he wasn't a coach Thorup worked with at Nordsjaelland because the coaches he had there wouldn't qualify.
Röhl brought two foreign members of staff but one had worked in England before and the other has been a head coach so they'd be fine. The rest of his staff are English.
Cifuentes took one coach to QPR and that coach had worked in England before.
Just doing basic research I don't think any of Le Bris staff at Lorient would qualify.
My knowledge on work permits is very limited, however there is definitely a pattern there.