Obviously it would, however phones run on battery power and having the microphone always-on would drain the battery fast, which users would most certainly notice and also care about (more recharging, phone becomes unusable due to empty battery a lot faster).

Keeping the recent and current state of technology and where it is heading in mind, I think it's fair to say that consumers care a lot more about being able to use their phone than they care about that phone or the apps on the phone to collect data about them.