That would be a better system.
One of my recommendations is that all the officials involved in access, including the minister if he's involved, should be identified in the reply letter to you. Let's not beat around the bush; there's a system here that isn't normally told to you.
But no, I don't think they should be. If they track, monitor, and profile your name, it should be grounds for appeal to the commissioner. You should have the right to complain about it, and you should have the right to say that this practice should be banned.