I suspect the controller assumed this flight would use visual separation, like everyone else, when it entered the landing queue; and the pilot expected to use ILS, like everywhere else given the conditions, when it entered the landing queue. The difference in expectations became apparent only when clearance was given, at which point there's not enough flexibility to accommodate an ILS landing, and it's hard to guess when there will be a place to slot it in. Diverting to Oakland and repositioning later is a reasonable, if not optimal outcome.
My guess is, if either side had mentioned their expectations when the flight entered approach control, and it had been cleared up then, it would have been quite possible to get an ILS landing on the first go round. (ATIS recordings did say simultaneous visual approaches)
