But I especially like your point that if you were to do that, you are giving a player the advantage of having the button for two rounds when we do not have to. I hadn't thought of that, and I think it is a good reason as any for keeping the rules different.
Another point along this line. When moving a big blind in and placing them in a single big blind spot, that table was only going to have a single big blind anyway. In a broken game scenario, wouldn't we be penalizing the table (albeit in a small way) by forcing them to only have 1 blind when they could have 2?
Button is in seat 1. Small blind in seat 2. Seats 3, 4, 5 are vacant. Big blind is seat 6. Utg in seat 7. Seats 8 and 9 occupied. The hand is played out and no one busts. Players from a broken table fill in seats 3, 4 and 5. Do you agree that seat 6 is small blind, seat 7 is big blind, and we have to play one hand six-handed, and cannot just allow the new players to start playing?
Yep.
If so, consider the same situation except that the big blind in seat 6 busts. If the movement of blinds is based on seat, then seat 7 will still post big blind, and we play one hand six-handed (five-handed if seat 6 is not filled right away). If however "position" is not by seat but based on button position, then seat 3 can post SB and seat 4 can post BB... But now seat 7, who was supposed to post BB next, miraculously now gets to evade the BB for three extra hands (two if seat 6 is not filled) when we did not have to give seat 7 that extra advantage. The big blind was supposed to move forward, and now suddenly has moved back 3 spaces... I don't think that conforms to a dead button movement, and I feel there are some parallels between the reason you gave to not play with one BB in a broken table situation, and interpreting the rule as maintaining the responsibilities of a "position" based on who can take the blinds after the button rather than considering the _seat_ being filled.
The big blind didn't move back, it just hasn't jumped forward. Seat 7 is still only paying that big blind 1/9 (or 1/8 if 6 isn't filled) hands which is probably pretty consistent with the rest of the tournament players.
If you flip that around the other way, is it fair for us to make seat 7 pay a big blind here after only having seen 5 hands when the players coming in would likely get more? Seat 5 would get to come in as the button and see at least 7 plus whatever they got at the last table.