While I would be in favor of something like that occasionally, that really takes out the match play element out of the round. For example, I watched two of KC's better players battle for tag 3 last year. Now lets say that in my group, tags 2, 21, 35, and 70 were in play. The two previously mentioned players may take some more risk, knowing that they're only playing each other for tag 2, and the loser would end up with 21 (or even 35 if they blew too many strokes by being aggressive). However, if all tags are in play, then 3, 5, 9, 13, and 20 are also in play, so you'll be more conservative, maybe end up with 3 or 5, but probably with a tag better than 21.
I think it would be cool if one league a month was an "all in" league for a reshuffle. This would be an unannounced thing, of course, therefore not allowing the good tags to sit at home 1 week a month.
