I thought of this also. But my experience with viewing a phone in the daytime leads me to think that I wouldn't be able to see anything on the screen. I tried using my Garmin Varia radar with a smartphone, and it was poor. The phone screen is wiped out on a sunny day, especially since I need to wear sunglasses when I ride.
Then I bought the Garmin Varia radar display unit, that uses bright LEDs, and it is excellent.
And that's what I use to "see" behind me. The radar unit I use is the RVR315, at $150. There is also a more expensive model that has a light built in.
The display unit is just called the display unit, at about $90. It's Garmin, so it ain't cheap, but I am totally happy with it. I also have a bar-end mirror to check as necessary. But the radar system is much better than a mirror, IMHO.