Thanks Ken and Nick!
K-Lo, yes I think I was thinking that the dedicated piece was along those lines.
And I too think it would probably be easier not to distinguish between the dedicated and non-dedicated, and just treat the new player as having come from a broken table, thereby allowing that player to (as per rule 9, Breaking Tables) take any seat including the button, bb, or sb, just NOT between the button and sb, in which case (s)he would sit out a hand and come in behind the button.
I think there would be complications with dictating that a nondedicated player be treated like when rebalancing (as opposed to broken table).
For instance, some venues will seat re-entries by taking them to different tables and sometimes giving them their choice of seats (as opposed to random). Then there may be a new player or re-entry who requires special consideration for seating. And then there is the case of a person filling a table from the standby list(which is really a dedicated seat and would fall in the broken table category anyway). Just to name a few.
All of which leads me to think like you that it would be easier to treat the new player as coming from a broken table and then allow the player
to play that seat according to the Broken Tables rule, which would allow that seat to be the button, sb, BB, or other, just not between button and sb.
One other thought - I agree with previous replies that feel it best to get a new player in the game ASAP. And furthermore, I think it is fundamentally better than to let a player take the button twice in a row when the new player could in fact be the button, making the previous button now be the cutoff. I know, this happens too with a dead button, but this is one less case of giving that player that advantage.