So for example if I want to book some Qantas flights (ie. classic rewards) to Singapore from the Qantas website, and then make a separate booking with Qatar or Emirates to fly from there to Europe, this is not possible?
Why do they do this, is it a protectionist measure to force people into flying with SQ?
This is because they have wanted to prevent people entering Singapore, essentially. Not necessarily a SQ protection measure, you can certainly book through flights from Australia to a range of destinations on Qantas or Jetstar (often connecting to Jetstar Asia).
Separate bookings are only possible with entering Singapore. So you could in theory do separate bookings, but would need to travel to Singapore on Vaccinated Travel Lane (VTL) flight, apply for a Vaccinated Travel Pass (VTP) and meet all testing requirements (pre-departure RAT and RAT within 24 hrs of arrival). Would want a reasonable amount of time between bookings as well (I'd say at least 5- 6 hrs).