Just came late to the thread. Opposed to eliminating sirens - strongly.
Weather warnings are one place we need all the help we can get. As has been pointed out - not everyone will have their electronics on in the middle of the night, and face it many of those same folks don't have weather radios. Or maybe they leave their cell phone in the car. No matter what you think of, text and internet still isn't patched into a foolproof broadcast method any more than TV or radio. It has to be on and nearby to work (or able to turn itself on and nearby).
Although tornado sirens were never meant to be indoor warnings, they fill the gap nicely and can be heard in many buildings. Used properly, they induce a kind of attention and even fear in some so as to induce action. They usually imply something dire is about to happen (unless over used). Text messages can be misread, misinterpreted, and don't always have that same feeling of urgency. Too many words leaves people interpreting and thinking, when some of them should be thinking "danger - get to cover now!"
As Mike mentions in his book (When the Sirens were Silent, but Warnings is excellent as well) both NWS warnings and sirens can fall short of the goal if used improperly. So again, I say the more warning methods to get the message to people, the better - in case one is flawed or missing you have the other hopefully as backup.