That's pretty much precisely what this is, with 10 heads visible (there are several other banks of cabinets), each of which can address, erm, access, only a fixed set of storage (a 20w x 25h bank of drawers).

Makes you think of total storage capacity vs. I/O bandwidth.

Or what would happen if the data required reindexing or sorting.

It reminded me of the automated tape library systems of the last century (I imagine that some of those might still be in operation).

Oh! That reminds me of an idea I had once for a “kid-powered computer”. Here is a sketch that I made to illustrate how a disk-drive works: https://flic.kr/p/an8kAA

You don't have any plans, by chance, of designing perpetually-running trains, do you, Wilfred?