I meant for the ATC to provide a descent estimate of when Lufthansa should be expected to enter the AERODROME TRAFFIC CIRCUIT (since you want tolink the FAA glossary) in order to land (they had them on a hold pattern for 35+ minutes). This is independent of whether the approach is IFR or VFR. A TOWER controller has all the information necessary to calculate that estimate, and should be expected to do so, the same way a stock trader is expected to calculate PnL of their positions on the fly given the current stock price.
Most of the queue would have been with approach, not tower. The aircraft sequenced to land were split across at least two controllers, tower and approach, and possibly more than one approach controller depending on how SFO splits them up. I would expect approach to be able to provide a reasonable estimate but it seems like in this case the estimate was found to be four minutes off, which seems totally within the bounds of a reasonable estimate from an approach controller.
The traffic pattern (US term) isn't really a factor here either way, airliners flying visual still usually use charted routes (like the instrument procedures) or radar vectors rather than the pattern. Remember that the pattern is only about one mile out from the field. By the time airliners are that close they're probably cleared.
> but it seems like in this case the estimate was found to be four minutes off
No, I don't think you are being at all accurate about characterizing that; maybe you lost count of the delays. After being told to wait ten more minutes, the pilots waited an extra four minutes before pressing for an update, and got told to wait another 10-15 (or f off).
Aerodrome traffic circuit is the ICAO term for traffic pattern, which is it what it is called in the US (it may be in the glossary but the point is that manual uses "traffic pattern" repeatedly). And this "traffic circuit" you refer to is almost always a VFR thing, as IFR approaches use specific charted procedures that generally do not end with a traffic circuit.
Aerodrome traffic pattern is completely different from holding patterns. And this is what LH was instructed to do, keep holding. Holding patterns are published for all airports and usually planes are stacked on those holding patterns and they are emptied FIFO style. Busier airports have multiple holding patterns to accommodate a large number of aircraft in case of on ground emergencies.
Sure, but GP stated wrt traffic patterns, "This is independent of whether the approach is IFR or VFR." which is not the case. For IFR, as was the case here, the LH was looking to execute an IFR approach, not ever enter the aerodrome traffic circuit.