Ah, okay - as assistants, I don't have any such reservations.
Take any Prem specialist or head coach that the incumbent HC thinks is the best fit - no problem.
I'd kill to have a Worsley, or an O'Gara as an England assistant coach, learning international rugby. If they take to it, they'd then have a shot at the England top job (as they've already got the club pedigree) - though even then, I'd prefer them to take on a lesser international HC role first.
On Baxter himself, I suspect that he's been too far from hands-on coaching for too long to make a good assistant coach with England, but I would not rule him out based on my suspicion.
I'd take Hepher or Hunter from Exeter with no such qualms.
If I had to lay down my ideal (mythical) career progression for an England head coach ID say:
Specialist coach at club level
Assistant coach at club level (different club, preferably overseas)
Assistant coach at international level (overseas)
Assistant coach for England
Head coach at club level
Head coach at international level (overseas)
England head coach.
Realistically, I'd want to hit as many of those as reasonably achievable with as much success as reasonably achievable.