That is very far from the truth. Just look at the scramble around power outlets in all sorts of public places from cafes to trains. People are desperate to recharge their phones.
Stories of phones running out of battery are now as much part of folklore as not having coins for payphones was a few decades back.
Go to any Android or iOS support forum and you will find that battery draining questions are a major category. And it's plain to see that it isn't just techies asking these questions.
Battery is also _the_ limiting factor for the tasks phones are suitable for. CPUs, especially on iPhones, are capable of so much more than what the battery allows.