While it's a bit extreme to say cycling computers are worthless, I somewhat agree that one can easily live a happy cycling life using just a mobile phone app, provided that you're not training.
I have the Garmin Edge 530 that connects to Ultegra Di2 via the wireless module and also controls my bike lights... and the combo is really amazing. However, when I ride I also run the Strava app on my phone as a "back-up" of sorts in case the Garmin flakes-out (which it does on occasion). Because I'm not training for anything and cycling is mostly done for fitness and enjoyment, I find I glance down at the Garmin on occasion to see my cadence, speed, gearing, etc., but it's not like I change anything once I read the metrics. What I typically care about most is my "post ride report"... i.e., how many miles did I go, what was my average speed, etc. As such, I can and sometimes do ride w/o the Garmin at all and just enjoy the ride, knowing that my phone will tell me what I did with "close enough" accuracy.
Phone Battery Saving Tip: If you use your phone to track your ride using an app like Strava, turn off your WiFi and BlueTooth antennas (or just use "airplane mode") prior to your ride to save your phone's battery. When you're out riding, especially in remote locations, your phone will suck-up a lot of juice hunting for network connectivity that you don't care about. As long as your phone's GPS antenna is enabled, Strava can figure-out your speed and distance. I also keep my mobile data enabled so that my phone sends my location data so my wife knows where I am in case of emergency. If you don't have someone "watching out for you", then I'd suggest turning off mobile data as well and just sync Strava when your ride is done. Also note that on Android, there is a toggle for "Automatically turn on WiFi" which you'll want to turn off or else you'll find your WiFi antenna magically turns itself on.