Because eclipses predictions were always accurate, sometimes to the exact minute or even second it will happen, and you can physically confirm they are right. Out of the dozens or hundreds of climate "prediction", we can physically confirm none of them has been true so far, not even close.

Correctly predicting an eclipse makes money, since people will travel far to see it and buy special glasses and such. There's no money in incorrectly predicting an eclipse, so even corrupted people will have to make correct predictions. Having someone stay healthy brings no money to the pharma industry. Having someone stay unhealthy for as long as possible, makes pharma very rich, so corrupted people have an incentive to keep people sick in any way.