For the reason rlcarey mentions, many banks attach copies of the checks to their copy of the hold notice solely to facilitate third party reviews. The regulation does not require it. However, as you have discovered, the number does not tell you everything you need to know. In addition to cashiers checks, the number in the MICR line doesn't indicate state and local government checks or payable thru checks. You do need the list of "local" numbers, it's just not enough to answer all your questions.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.