I feel like it is still a tournament set and if people throw it then that's on that particular person. It is still a tournament match being held for a placing in tournament the same as every other match held in the bracket.
Even if people know they are not going to place in the money, they still try for a higher placing in bracket. I do not really see the difference between those matches and playoffs, but what do I know..
Would playing out 5th and 7th feel more legitimate if we played them out before winners/grandfinals?
That way we could avoid that feeling of "oh the tournament is over but I still have to play a match." and replace it with "oh I have another chance to improve my placement in this tournament."
I don't think it really matters if it is after the tournament or not. The thing that is important is that the player's placing in the tournament has already been limited. If you have been eliminated from the tournament, it is no longer possible for you to get 1-4 (as for fifth place ties). If you're playing in tournament, you have the potential to get first place. That seems to be part of what a tournament match is. Less rides on the playoff match than a tournament match, because there is no further potential. The playoff and the normal tournament match definitely seem to have different characteristics.
Now, the other type of matches (other than tournament) that we include in power rankings are money matches. A playoff is solely a contest between two players. There is nothing after that match. A money match is solely a contest between two players. There is nothing after that match (well, they could money match again, but that has no causal relation to the previous money match). Now, it seems that a playoff seems to be pretty much the same thing as a money match. The reason a money match is considered comparable to tourney sets is because there is money on the line. Is it stupid that we make this the benchmark for determining that money matches count? Perhaps. But either way, we still count them.
So it seems that there are two things that validate whether or not matches count for prs. The first is if it is a tournament match. As I defined earlier, a tournament match is a match where the result has an affect on future matches (a causal relation). The second is if there is money on the line.
So it seems that the only way to make playoffs count for prs is to either put money on the line or make it have some kind of causal effect on the other matches. Seeing as the two players are already out of the tournament, you can't really do the first. So the only option left is to put money on the line. This is why I think we should not count them. Unless, of course, we change what we accept, and also include challenge matches (which I think is stupid for other reasons).
Now, the main thing that people will disagree with me on is my definition of a tournament match. I suppose a simple definition like: 'Any match that happens in tournament' is what you guys are thinking of. However, it seems stupid to me that every match (with the possible exception of grand finals) follows one structure and this one particular match (a playoff) in a tournament is different.
Either way, it doesn't matter too much to me if you do playoffs or not. Playing more serious matches is fun, and I think that I should try either way. I'm bringing this up from a pr perspective. I think counting these matches without money being on the line corrupts the data.