I also find this odd. Why can't the security staff at step 1 be trained to check that the name on the boarding pass matches the passport being used? This is done at HKG and many other airports around the world. In the US and Europe, security is the only check in most cases.
I would also add that SQ, BA, QF and others check I'd against passports at the gate. How many checks do we need?
The more I think about this, the more this seems to be an example of agencies in SIN not talking to eat other (or being unwilling to cooperate). It's not as if the checks made after the automated barriers are thorough. In fact on one occasion recently the security person after the automated barrier let me through based on my boarding pass and looking at my India visa (which has a photo printed onto it).
I generally love SIN, but this is one area of operations I find strange. The other is the lack of effective priority security at gates when 500+ passengers are trying to enter the gate area. Airports with similar layouts, such as AMS, manage to do a much more effective job with this - and airlines generally use the service, which means the airport is charging a reasonable amount for it.