The only time bizarre demands happen imo is when somebody offers a contract, retracts, and then that player is delayed in dropping his demands. But apparently they fixed that, and ever since then I can't recall wanting a player but finding his price to be unreasonable. If I'll pay a guy $500K, i'll probably pay him $1.5M so it doesn't make a huge difference to me either way. wrt type A status, i'd rather have it last through the draft so people don't want until day 1 of the regular season to circumvent compensation.
I think the current FA system is perfectly reasonable and it's never bothered me at all, really.