Probably the system design starts with Cat C and D types, where there is several seconds of inertia, and where the main landing gear is expected to straddle the centre line at minima and one dot deviation. Also the PF might not be able to see the runway from his side on an offset.
The IGS Runway 13 Kai-Tak was on the chequerboard hill, so presumably minima was 200 feet or 250 feet above the hill elevation. If as customary on a difficult approach the PF was FO am wondering how the Captain as PM might have taken over the landing? The FO having a betview of the threshold.
I think the issue of higher minima for offset approach is rather where to expect to see the runway? although anyone crabbing in slow GA aircraft will tell you +/-20deg is very common, the Archer Century AP used to disconnect on those scenarios 
Peter wrote:
340ft is probably what you can get with an NDB…
Almost. The system minimum for an NDB approach is 350’.
300’ for NDB/DME.
This is quite funny because it is not difficult to turn an aircraft by 5 degrees (or even a lot more) at 200ft
But it makes the ILS worth a lot less. 340ft is probably what you can get with an NDB…
Peter wrote:
Is there an additional factor if the LOC is offset?
Yes. According to PANS-OPS the minimum approach category A OCH is 340’ (rather than 200’ for a regular ILS) if the final approach course is offset more than 5°. The increase is even higher for other approach categories.
Is there an additional factor if the LOC is offset?
We did this before [ threads merged ]
Maybe the design is done for a 2.5% achievable climb gradient?
Didn‘t do the math, but missed approach track says „turn right as soon as possible“ which takes you directly above a 110ft obstacle. So OCA of 430 feet doesn‘t sound too wrong. 200ft would be clearly too low (and is typically only found at approaches where the missed says „go straight ahead (over the runway) when the tower is far enough from that runway)
Peter wrote:
I often wondered why the UK has DHs like (EGMD ILS21)
ILS21 OCA = 430ft is probably higher as it’s offset ILS not stright-in (due to Danger Area D141 which I was told sits at close as 3/4 LLZ scale deflection, someone tested that for sure), 100ft agl obstacles punching from bellow at 1DME on tight missed approach turn away from DA044 and 400ft agl windfarm, funnily enough NDB21 OCA = 420ft, go figure 
I did one IMCr revalidation there, went missed somewhere near 750ft with all safety addons just after we reported 3nm
