Depends on the use case, really.
My car is from 2011, so I have to set its clock manually, which means I have to adjust it twice a year because of daylight savings. It’s a little over a minute ahead of my phone (iPhone SE, so uses Apple’s time servers), which I think most people would find acceptable. For real-world personal events, not even accuracy down to the seconds matter that much.
But people do need some accuracy (as in, their clock can’t be 20 minutes off), or their alarm won’t wake them up at the right time in the morning, and they won’t catch the right bus.
For banks, it’s an entirely different story, as their servers have to agree on when transactions came through, and in what order, even if they were handled by different servers and happened 1 microsecond apart. I don’t think they use the pool though, given how accurate their time needs to be. They probably rely more on whatever local government institution is in charge of timekeeping, served through a dedicated fiber connection.
I have very little sense of time and how it’s passing, which probably is related to my interest in having (all the) computers keep time really accurately.
I’m autistic, and have no way of judging the passage of time except on the grossest of scales. Time has been a Special Interest for me since I first noticed the ticking of an alarm clock long before I could speak. When I answered the phone when a radio listener survey called (you can imagine how long ago that was) and was asked “What’s your favourite radio station?” I answered “WWV”, which was the US National Bureau of Standards (now National Institute of Standards and Technology) time station. Every room that I frequent in the house has a wall clock that sets itself using signals from WWVB on 60 KHz, all of my wrist watches do likewise, and there is a Pool server withing arm’s reach at this moment. Every computer in the house is within +/- 8 milliseconds of The Time.
It’s the reality that a lot of people don’t know how the world works. They just care whether the functions which they need work or not instead of the mechanism behind. They are at no fault at all because everybody has his/her own priorities.
Different people do different things to keep our world moving.
For myself, I run NTP servers to serve the pool just to help the internet a little bit. I personally don’t go extreme on timekeeping though.
I grew up with BBC pips at the top of the hour, learned about WWV and used to listen sometimes daily to set my analog wind-up watch and figure how many seconds it lost each day (I even tried to adjust the spring to improve it).
Now I just want to have the precise time so I know exactly how late I am for everything. =)
And my latest watch, a Citizen Eco-Drive self-charging quartz, keeps the best time of any wristwatch I’ve had.