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.
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.