I think you severely underestimate how often this happens. I know teams that want to do well in the cup that have bought players in a rush to try and secure a victory. More commonly is the last minute rush before playoffs where many people are trying to get a last minute superstar to increase their chances of promotion, or simply to avoid relegation. Hence why prices are often so much higher during the week before playoffs.
I know prices change before the playoff, but most of the managers buy players to keep, not like Superfly who constantly changes his lineup. Great team has better chance at selling high aswell, why? because people tend to think he must have superb players, not all of those players are great, we could almost call it daytrading. How would player tax interfere with people buying higher. It would just tax players not sold.
So what you are saying here is you don't mind people constantly listing "overpriced" players as long as it is only once a week?
I'm not saying that removing players from active list during TL time is the best idea, but it would "help" with the constant listing problem. I still think taxing not sold players is the best way.
Ofcourse there are different users and different needs, but you need to get this: there is a certain player value, nomatter what you think the player might be worth. If a player is valued about 1,2-2mil for example you think he is worth 4mil to you because he is australian. Now there is no TPE for him. He is listed at 1,5 at the start, now some players have bid on him and he is at 1,8mil, will you go and bid 4mil for him from the start or is he really worth 4mil? Now if he is listed at 4mil and you go and bid on him alone, it does not show he is worth 4mil, it shows you have no idea what you are doing. Players skills determine the value. If you overbid on something, it needs to be noticed and transfer price fixed. You will lose your 4mil (for bad management) but the sellers received money needs to be adjusted to prevent cheating.