A Verdant event causes way too much damage and requires far too many resources to realistically contain. The massive resources required and the large-scale and fast labor needed to do everything quickly enough to maintain the Veil fall into the unfeasible and impractical. In situations with smaller events requiring less resources, the Foundation has wound up going with "destroy the town, invoke cover story" since it just requires too much otherwise. The Foundation's resources are vast, not infinite, and they are still generally bound by normal time.
The Verdant events as described are such that slipups would be unrecoverable for the most part, and would tear at the Veil.
There should also be mention of the Foundation looking for methods to appease the deities in question, on the reasoning that if the wind gods are in a good mood, maybe they'll knock off the events, at least long enough to find a way to contain the gods. (It's a lot of resources to contain a god, but much less than what it would take to believably cover a Verdant event.)