How does the service know that you're in possession of the key unless you give it some kind of input about the key that's unique to the key and to the current time?
Lets say you've got a 'fob' which is plugged into a USB port. Application sends the fob a challenge, fob responds. Application validates the response and proceeds. Perhaps the key uses 2.4mhz wireless, perhaps it uses bluetooh (a protocoled 2.4mhz wireless solution :-). The benefit is that these things can only occur when you're key is present. No key, no transaction.
We don't worry about Nigerians stealing our cars, but we should consider what they might do with our self-driving cars if we don't have some durable way to say we're in the car right now.
I appreciate that you prefer having something like this on your smart phone, but such a solution fails for the larger internet population. And while SMS works for 'dumb' phones you cannot have it validate on every send, every post, every tweet, every page view.
You may not share my urgency on this as a threat but I invite you to start to watch more closely. In the Atlantic article a Google representative said "Thousands per day" this is big business for folks. I was talking with a senior executive at Wells Fargo who mentioned hundreds of millions of dollars 'lost' every year. This is a growing problem, its getting more expensive, and like some digital herpes my expectation is that it is going to pop out suddenly in boils of financial putritude dripping pain, financial suffering, and expense for everyone involved. With luck we'll fix it before then but most folks who are getting burned are more interested in covering it up rather than addressing it sadly.
I think it would be wonderful to have a possible solution prototyped and demonstrable for people in pain. Your passwords will be compromised, and if you do anything financial online you will have money vanish and you will experience arguing with a bank as to why they should give it back to you and take the loss. This isn't a 1 in 10, or 3 out of 5 type statistic, I'm pretty confident that every single person who has an online account which can tranfer funds (whether its an iTunes account or a checking account) will experience this. 100%.