Anecdotal, but personally, this is one of the most refreshing and cherished qualities about my exercise time: it's ME time. No messages, no phone calls. Phone goes on airplane mode, and I'm in my own zone for those 60-90 minutes.
After reading My Year with a Distraction Free iPhone* I took steps to drastically reduce notifications and social media apps from my phone (not as drastic as the article, but way quieter than before), and I feel happier for it.
Maybe it's just me, but MORE notifications, messages, and calls to my wrist sounds like exactly what I don't want.
* https://medium.com/time-dorks/my-year-with-a-distraction-fre...