In my experience it's rare to see a ruleset as hard as "absolute cheapest, no exceptions" - generally what I see is "must be within percentage of absolute lowes

In my experience it's rare to see a ruleset as hard as "absolute cheapest, no exceptions" - generally what I see is "must be within percentage of absolute lowest price". Even within these restrictions loyalty programs still make sense - these are people who purchase a large amount of travel per year, if you can guarantee yourself as an exclusive supplier you still come out ahead - even with price ceilings.