Not necessarily. Only di Matteo has managed it recently. Here's a list of the managers that have taken teams up in the last 5 years
Mackay
Holloway (twice ffs)
Allardyce
Bruce
Lambert
Warnock
Coyle
McLeish
McCarthy
And here are the names of the managers of the current top 7 teams...
I do agree with the OP. Our style is far more suited to the Prem than the Championship. We are far too negative at home with our formation - our away games haven't been too bad - but we have to find a way to play two up front.