"Just get a bike computer, it will do distance, time, average speed just like your phone, and it will even do more, like cadence!"
Firstly, computers don't show cadence unless paired with a sensor, true? 2ndly, there are several cell apps that most defnitely display cadence when paired with sensor. The pros & cons have already been listed. Get a computer if you want compactness, better display, less expense if crashed... but don't get a computer thinking it's doing more than the well featured popular cell apps... even without a sensor.
As far as waiting for breaks to look at the phone.. I'm not sure I understand.
I'm using Wahoo Fitness paired with DT and have the phone displaying realtime readouts the entire ride. I don't take breaks to look at the phone... a quick glance and I see Cadence, HR, Speed, Distance, Time. I have no problem seeing the display in bright daylight and the Wahoo layout is great.
A quick slide to another screen shows elevation gains, grades, climb.. slide the other way to see the map. There's a lap times page also that grab snapshots with one touch operation if you're doing intervals. The touch buttons are simple (Pause/Resume toggle), large and easy to use.
Personally, I don't touch the screen.. once I start the workout thats it.. I leave it on the primary display and it never turns off. I have audio readouts calling out my last 5 minute averages, and audio on the mile intervals calling out the overall totals and averages.. so I rarely look down other than a glance to check on a reading. To me, the Audio Read-Outs is HUGE. Not sure if the computers have that feature. When the workouts done, touch Share/Strava (or whatever).. bang done.
I'm not trying to convince anyone NOT to buy a computer.. I'm correcting a lot of misinformation regarding the features of cell apps paired with sensors. If you don't have a computer yet, but, you have a smartphone.. try the Wahoo app simply using the GPS. You might like what you see until you figure out which computer to buy.