I sincerely can't see whats the big problem with auction sales
It opens a possibility to transfer money between teams.
if it's working good for players it can also work good for picks in my opinion.
It can, if it follows the same rules and receives as much attention from the users. As I wrote (in not so many words), the chances of controlling the fairness of the system depend greatly on selecting between an open market and a closed one. If the market were closed (own league only), the only eyes on the sales would basically be the league mates. All other control would need to be automatic.
What you need in order to put more eyes on the transactions is an open market. Even then, it is pretty difficult to judge what a fair price for the first pick or the Nth pick would be. I guess the market could in some sense decide it by itself, although what we are seeing with staff bidding (see level 5+ coaches) is not very promising. So, it would perhaps make sense to introduce a level of blinding into the system. You would then not know whose pick you are bidding on, only that it is e.g. the first pick overall. That removes any motivation to bid higher than necessary. Obviously, any system where you could draft outside your own league would be problematic with the current scouting system. Should be doable one way or another.
But anyways, adding a buyout option might eliminate a case in which picks are being sold for "too much"- the highest price for a pick will be lets say 1M, the moment someone offers 1M (or any other price chosen by the devs) the pick will be sold to him immediately.
A maximum does not keep anyone from cheating if the money is good. If it isn't, why would anyone sell for the maximum or for even less? I'm not saying this is completely impossible, just that I don't see how it would really work in a reasonable way.
A friend of mine also offered a system in which every pick will have it's own (chosen by the devs) price and the selling team will only get to choose wheather or not to sell the pick and not the price, and the first team which is willing to buy it and has enough money win the pick, I personally think this option is way worse than an auction and will open up much more cheating possibilities.
Something like this might actually work better in terms of preventing cheating. You could perhaps structure it such that the 16th pick overall has the chance to buy (or trade picks for a price) the first pick (if available) first. If they are not interested, then the 15th pick and so on. And next, you consider the second pick and so on. The problem is that building such a structure gets complicated. And perhaps more importantly it's just not so trivial to actually set good prices.
While sales or trades of draft picks is realistic, I'm not sure what purpose it would serve in this game. The positive thing is that it would allow a little more chances of rebuilding for teams that do well every season. Now they have little to gain in the draft in any active league, which makes the draft rather uninteresting. And perhaps it offers a steadier income for those teams that get good bids but are not interested in the draft (although why wouldn't they be?). So, there would at least be a bit more strategic freedom (usually a good thing). But the sales issue is not without problems, as seen above.