It all depends. Yes, you can go without a watch, but there’s plenty of places where being able to tell the time is very useful and clocks aren’t always available; moorland, forests, mountains, etc., needing to know sunset and tide times…
And yes, my phone has the time on it, but if you’re on the bike, in a hurry to get somewhere for a specific time, trying to fish a phone out of a pocket or backpack is a pain when all you need is to glance at your wrist. I have a TAG Series 1000 black finish with a luminous face I bought twenty years or so ago, for £250, which has been hammered unmercifully, the black is worn off the case and strap and there are scratches in the crystal, and it’s still working fine. I also bought recently a MWC G10 milspec watch with the Tracer T3 luminous markers for £85. Excellent little watch, keeps better time than the TAG, the self-illuminating markers and hands are amazingly bright, and it seems pretty tough. Looks quite smart, too. I’d recommend one to anybody.