It isn't elites(in Indian case, at least), quite the opposite.
It's engineers - it's simply easier to get required specs with f404/f414, it's going to be easier later to work with it (reliability, etc).
"no one was ever fired for buying IBM". f404/414 work, they're installed on thousands of aircraft around the world, etc etc.
Eurojet can run in circles about how advanced they are, but GE is probably the best technical deal in the world.
RD33 is a well known trouble to work with, though new mods are much better; it is just a way less advanced engine (early fighter turbofan, conservative design even for its time, and on top of that - one optimized not just for performance, but for rough field ops).
But it is available to India without questions, it is in Indian fighter fleet for decades, and you can buy full spec for it (WS-13) and develop it further, unlike the endless dream of kaveri. But yes, as an engineer you'll have to step on your selfish side.
Which is hard to do on a plane so full of western (sanctionable) components, why you should be risking your head when others don't?
Others managed to go for less toxic suppliers, though.
Airforce officials and below(pilots, former and current) are another big group.
For them it's straighforward prestige - same kind of prestige that is gained by driving expensive western car.
This played at least some part in Rafale choice, for example - Rafale is a prestigious "car" to drive; remember our Indian friend here, who was seriously proud of nation's premier fighers price (frigate pricetag per jet which isn't NGAD, yes) and source. Western engine is smaller, but it is still a similar logic.
