I had a colleague that would come back from vacation, see 1000+ emails, and just mark all unread emails and hit delete. And say "If it's any important, they'll just mail me again".

Not saying that it's a good way to do things, absolutely not, but it did open my eyes to the fact that some people will just indiscriminately delete emails, no mater how important they could be.

Well, odds are none of them is important. And they are probably right in that if it's important, the sender will look for them again.

This person just got 1000 emails in the time of a vacation. How viably is it not to completely ignore that? It's even surprising that they bothered to look and cleaned up in a way that implies they aren't ignoring them on the daily work.