For SMS, though, the reader (often a mobile phone device) has to read the message the moment it arrives (or it, well, won't arrive). Since tweets are not limited to one person, reading Twitter can happen asynchronously.
If your device is off when your network gets an incoming SMS, the store-and-forward system just holds it until it can be delivered. This is exactly the same behaviour as Twitter or indeed e-mail.
My carrier can send SMS to multiple devices, or I can pick them up via a web portal, or via e-mail.
...yet.
Sorry, I'm not much of an SMS user, so I lack sophistication with it. And I sometimes forget that my personal quirks are not generally applicable.
While I'm correcting myself, let me note that sending an SMS costs money. That money may add up if you're blasting SMS messages to 10k customers at once. Of course, we're discussing the possibility that Twitter may end up costing money too, but perhaps it will still be cheaper.
And they don't get spam filtered, nor do I get phishing Tweets from people pretending to be my hosting company.
Remember all those harebrained schemes to charge companies tiny amounts of money for guaranteed-delivery emails with verified sender IDs? Twitter just deployed that system right under our noses.