Hi Anthere
Checks should be done only on accounts doing abusive edits to Wikipedia (vandalism, insults, spam, defaming etc...) If checks are done without any relevant reasons related to abuse, then those checks are abusive and the person with the checkuser access should (will) lose it.
Just like admins wrongfully blocking accounts are also supposed to have their admin status revoked? Please realize that the two actions have very different worst cases.
Blocking: Worst case: You do not get to write in Wikipedia for a while.
IP Checking: Worst case: Someone who doesn't like you get your ip checked, calls your ISP and talks with a clueless receptionist who reveals your real life name. That person then publishes your name somewhere. Your boss who happens to also be a Wikipedia user finds out about it and fires you because s/he think your political stuff you've written on Wikipedia suck. So some brat on WIkipedia cost you your employment.
You don't even need to be an ArbCom member to do that. Let's say a veteran editor like Ed Poor asks for an ip check. Will an ArbCom member oblige? Yes, because Ed Poor is trusted. So your only job is to convince Ed Poor to ask for an ip check. For more details: http://en.wikipedia.org/wiki/Social_hacking With the checkuser tool it becomes so much easier.
If you have ever met a political refugee, you know that they often are very careful not to talk politics with persons they don't know. Especially not with strangers from their own home country. The reason is that they fear secret agents from their home country. Often this fear is unfounded paranoia (there aren't THAT many secret agents in the world), sometimes it is not. Their worst case checkuser scenario is even worse than the worst case scenario I described two paragraphs above.
That's why I hate the checkuser shit - (mis)uses of the tool can have very detrimental real-life effects on real-life persons. Something that nothing other on the silly text game Wikipedia can have.
-- mvh Björn