The statement "Why are SQ fares typically so high" seems too much of a generalization as far as I can tell.

For example, I can get ICN-SIN-LHR for USD650, when Korean Air and Asiana charges far more. (and USD650 is not dramatically higher than other foreign carriers' fare on the route)

LHR-SIN-SYD is another example: You can get specials for around GBP600-700 which is very reasonable. Again, not much higher than the typical cheapest fare on the route.

They have lots of specials on routes such as NRT-LAX and FRA-JFK (both around USD1600 in C class, simply an amazing fare).

So it really just depends on where they feel they can charge more and where they feel they need to knock the price down. All airlines do this and so this is not unique to SQ.