I don't get the undisclosed fee - I am sure it is registered somewhere, but as you say it is not very transparent
I think you will find all fees and aspects of transfers, including players contracts, have to registered with the FA. It's probably the fact that that doesn't satisfy the curiosity of fans that is frustrating for some. From the clubs perspective, why would they want to broadcast what they pay for a player as that can be used against them in other negotiations.