I'd say in a test environment you should let it crash a lot. But in production, facing users (which can be another programmer, who suddenly forgot that he is a programmer and knows what you are dealing with) there are few situations were you should really crash.
Think about a very dumb user application like Word. Let's say word crashed with a Stacktrace, some log messages, the best error message ever, maybe even saving the user data in a backup file somewhere. The user will think Word is unusable.
Now let's consider a scenario in which Word recovered under the hood by losing the users data but never losing the GUI. The user still thinks it's bad, but he won't think it's unusable. To some degree he will blame himself for not saving the data himself.
That's why I think I would be way less willing to crash in front of the user and would apply Pokemon Error Handling (Gotta Catch them All) in all user facing software as a feature, not a bug.
In the context of the blog post - Erlang - "Let it crash" almost never means "let the entire application crash". It means "let the current [micro-]process crash, then its supervisor will restart it in a known-good state" (and if the supervisor crashes then its supervisor will restart it, and so on).
Enough of this and it will crash the node. You need to design for this in an Erlang system.
The ever-helpful jlouis has some useful writing on the subject: http://jlouisramblings.blogspot.it/2010/11/on-erlang-state-a...
As well as these: https://github.com/jlouis/fuse
Sadly, this is not discussed as much as it should be in Erlang land.