I've had the occasion to send out requests for FOIA logs to several local units of government. Here's my varied experience with these requests. I'm not certain that I have perfected the standard query, and so you shouldn't necessarily show the non-responsiveness of any given agency as a ding on them - it might be me.
The FOIA log is a set of records associated with FOIA requests. Typically I've been asking for copies of FOIA request letters, the cover letters of responses that are sent back, but not the full details of the relevant documents. If something particularly interesting comes as a result of this expedition through public records, a second request should be straightforward since you know that relevant records exist because someone else already got them.
One of the possible problems in asking for FOIA logs is if the public body in question has multiple parts of it that answer FOIA requests, and your seemingly simple request has to get allocated to multiple places. I think this is the reason that both the City of Ypsilanti and Wayne State University asked for more than $60 in fees to retrieve a month's worth of logs - I think, but am not certain, that the fees reflected the need to go both to the administrative side of routine FOIAs as well as to police department FOIAs for the same period.
The bright spot in all of this has been the City of Ann Arbor, which responds promptly and without fees for requests for city FOIA logs. Every single request is numbered, so that you can be certain that you're getting the whole set, and I specifically didn't ask for police logs in that case.
My naive assumption going into this was that every agency would be able to produce a stack of letters that they had received for FOIA requests with minimum cost and minimum search time. That proved not to be the case. I'll need to dig deeper the next time I send such a query in to make sure I'm not inadvertently asked for too much.