Usually, "not taking the entire service" does not merit an upward price adjustment. This is different for flights where "taking less service" (in terms of hours in the air) is something desirable and customers are prepared to pay a premium for.
It's not city-specific price disrimination, but pricing for a different prodcut (nonstop vs connecting). It is not anti-competitive, but, to the contrary, adds to competition. Because BA is able to offer AMS-LHR-SIN at a low price, KL is forced to cap its fare for a direct AMS-SIN. Overall, prices will be significantly cheaper. If you force BA to offer ex-EU connecting flights at a price that is not cheaper than the direct flight from LON then prices would go up everywhere, because "home" airlines would have a quasi monopoly.
For that reason it is important that airlines are able to protect their ability to offer different fares from different markets.


By the way, the fare recalculation language is already in the BA terms:

3c2) Your ticket is no longer valid if you do not use all the coupons in the sequence provided in the ticket. Where youchange your travel without our agreement and the price for the resulting transportation you intend to undertake is greater than the price originally paid, you will be requested to pay the difference in price. Failure to pay the price applicable toyour revised transportation will result in refusal of carriage.

3c3) If you want to change all or part of your transportation, you must contact us beforehand. We will work out the revised fare for your changed transportation. You will have the option of either accepting the revised fare or maintainingyour original transportation.