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The biggest problem is that once people got used to this sort of thing they would never visit your site. You could be churning out tons of emails but your traffic would be down.

And lots of emails isn't a good thing these days. Even if you have a dedicated server there are fairly strict email limits to avoid spam. As soon as anyone marks an email "spam" then boom - all your emails to that domain go into spam filters.

Finally there's a new belief that younger users don't use email at all.