Now it's just a matter of time for what? For Alice to enable remote access on her machine and set the mandatory pin? How does this help Eve?
Moreover, your scenario presupposes that Eve has Alice's Google credentials. At that point, Alice is already owned. Given that most of a user's information is online instead of on a particular device these days, accessing Alice's desktop is not significantly useful. Eve can already pretend to be Alice and send trojans to her friends and then pretend to be Alice's friends and send trojans to her.
Moreover, your scenario presupposes that Eve has Alice's Google credentials. At that point, Alice is already owned. Given that most of a user's information is online instead of on a particular device these days, accessing Alice's desktop is not significantly useful. Eve can already pretend to be Alice and send trojans to her friends and then pretend to be Alice's friends and send trojans to her.