that example SIN-LHR, I searched and found SQ at $1600+ and Lufthansa at $900+ which is a BIG difference, so that 8% cashback is actually more accurately valued at 4.8%
SQ offers direct flights, while you need to transfer at FRA for LH. Have you taken into account of that?
Also, the $900 fare you quoted for LH, does it allow changes/refunds? For curiosity sake, I did a sample booking on both carrier's websites, for SIN-LHR one-way, on 16 Nov 2017.
SQ:
$1877.70 incl. taxes and surcharges, booked into "Economy Flexi". Direct flight. Free changes, Cancellation at 150USD.
LH:
$1193.70 incl. taxes and surcharges, booked into "Economy Basic Plus". Transfer at FRA. Changes at 130EUR, Cancellation at 190EUR.
$3293.70 incl. taxes and surcharges, booked into "Economy Flex". Transfer at FRA. Free changes and cancellations.
I'm aware there are cheaper flights on LH, but they were codeshare flights and operated by Swiss Air. Even those have transfers at ZRH. I took LH operated flights for comparison's sake.
From the above we can see that the fare conditions are different for each carrier. SQ award tickets, even at saver, allows for free changes and charges a token amount for cancellations. Comparing the same fare condition, we should instead be looking at the flexi fare for LH, which costs $3k.
I'm not trying to prove you wrong or whatsoever, I just feel that a fair comparison should be made (ie apples to apples) when calculating the "value" of a mile in a redemption. Cheers.