I can't tell from the site if your card data is stored on your phone or not. If it is, then you're going to have to replace all of your cards if you lose your phone.
Also, shouldn't the merchants be checking the signature on the card?
This is the biggest downside in my opinion. Theoretically any merchant should deny any card without a signature, End of Story. In the merchant agreement they sign with Visa and MasterCard, they agree that any fraudulent charges where they did not check the signature are their responsibility.
How often are the cashiers checking the back of the card? Many of the card readers I see are on the customers' side of the counter, and I swipe it myself, often because I'll enter a pin. Also there are self-checkout kiosks with little or no supervision. I don't think that the lack of a signature line is the _biggest_ downside.
They should but only 40-50% do, I write "Ask for ID" on the signature portion. The ones that read it, ask me for it. Better than a signature that a cashier won't question anyhow.
I was curious about this and browsed through their operating regulations. It says something to the effect of "Visa considers a signature box that only says See ID to be blank".
So the pedantic response to your second sentence is that they consider the See ID irrelevant (and once there is a signature, it is apparently a violation of the merchant agreement to ask for ID, but I didn't look for that in the operating regulations).
Also, shouldn't the merchants be checking the signature on the card?