I am rather wary of getting involved in this however I'll try a toe in the water. I would stress I am not an arb com/en wp checkuser - I do however hold elected rights on three projects currently. My background (& I agree with everything that Andrew has said) is on en wb. The vast majority of checks there are on vandal accounts or impostor accounts (memorably Cary Bass!). In this situation the rights should be used vigilantly by a trusted admin watching RC. Equally a block of an IP can be made as "vandal source" (indeed with intelligent use of the log frequently "cross wiki vandal source") assuming it is not an open proxy which is often the case. This is visible and if the community require more info they are welcome to ask. I would never reveal private info but I would reveal as much as I could.
Vandals aside one real problem I see with public "request for CU" is that it is actually almost impossible to prove that someone is not a puppet account. Percentages of likely or unlikely maybe but not "no" - as such a public accusation cannot be cleared. I work on the basis that 25 or more people felt that they trusted me to use the tools in the each of the community's best interest & I would like to think I do just that. If I see something that concerns me on wiki I may well look, if it is obvious I will act, if there is a question I'll share with fellow CUs and ask them to review it. If there is nothing then that is it - no fuss, no accusations.
As a minor example I spotted some rather odd voting on a deletion request on Commons recently. No CU request was made. However it concerned me. I discovered of six people voting, one was a faked user and three of the others seemed highly likely to have been the same person (sock or meat). If someone tells me I am wrong to have done this then frankly a request for removal of my CU rights will be in on Meta shortly.
I'd like to think I had not got the wrong end of the stick on this and I stress I am not an en wp/arb com CU merely someone who's communities have trusted to deal with some cleanup work. Thanks for your time.
Herby