"Ms. Mayer resigned from Google on Monday afternoon by telephone. She starts at Yahoo on Tuesday." - That's quick.
For upper level executives as soon as you resign you're escorted out the door by security and you're not allowed to touch anything. The level of access you had was so high that they don't want you learning anything more about the company's plans and want you out asap.
I doubt anyone cared that she resigned by phone.
(my opinion)
In most cases 2 weeks is a professional curtesy.
Also, once they've resigned, they're no longer an employee, so for a lot of companies (Google included) they may not be allowed in the sensitive office areas, anyway.
Let's keep in mind this is also someone who is leaving voluntarily, not being laid off. They are picking their moment when they become a non-employee.
I think that particular practice is security theater - it's so the employer can say "We take all possible precautions", regardless of whether the possible precautions are effective.
Is it mostly for form? Probably, but there's a reason it's considered the right process. It's not done for "theater", it's done because sometimes these things end up in court later on.
There's no particular reason for that effective date to be "now" vs. "two weeks from now". I've certainly had coworkers that announced their intention to resign 2 weeks or a month before their actual departure (actually, the one time I've quit a job, I think I stayed for a couple weeks afterwards wrapping up my project & transferring knowledge). The difference is only that in one case, the employee is intending to resign but you don't know about it, but in the other, the employee is intending to resign but you do know about it.