We didn't exalt Lydia, and Alchemicals/Dragonblooded are a sort of special case. The alchemicals do get picked, but the guy who invented the idea in the first place designed him that way. Dragonbloods aren't guaranteed to exalt, but their propagation mechanism is also from a collaboration with another primordial and designed to do that.
The other exalts are very much not; the opposite is in fact the case because the gods couldn't resist primordial orders.
For their entire history multiple people tried to direct exaltations and the best they got is changing the selection criteria before letting them run around on their own. If biasing it like this worked reliably then the history of how everyone ever interacted with them would be very different. The occasional fluke appearing to work doesn't require everyone between the age of legends and now to be an idiot, while the reverse does.