I am convinced there are many reasons to buy it;
You are, but that doesn't necessarily mean everyone else is. There are many people who aren't comfortable with investing money on wearables and making something less familiar is not the way to go. By providing quality and reliable time keeping, Apple's assuring people that it will function like the wrist worn device we're all familiar with, but with exciting new features. It's why they reference watch vernacular and have positioned it like a fashion accessory with functionality.
How often are you surprised by the time your phone shows? Are you often "off" by more than ten minutes?
I don't understand what the point of this question is. I'm not usually 'surprised' at the time my phone shows because I look at the time when I want to know the time, not to compare the time with what I think it is. If you mean how many times have I thought 'it's earlier / later than expected' then I don't know? Probably twice a day or so? By more than ten minutes - lots of times, 3 hour parking is hard to gauge for example without checking your phone every now and then, especially when you're focussed on other things.
The notional Apple Sport would have alarm and reminder functionality. It could notify you that an 8pm event will occur in 35 minutes, but it would leave "it is now 7:25pm" as an exercise in mental arithmetic. Note that your current equipment displays Now 7:25pm and Event is at 8pm, but leaves the 35 minutes to your mental arithmetic, and that you are not on time as often as you'd like. These may be tied together, somehow.
So any time you need to know the time and you want it displayed on your Apple Watch, you need to have an alarm set? Say I need to catch a train at 7:23 AM - I would need to set an alarm to know what time I have to be at the station by. In fact I would need to set up multiple alarms to know if i'm on track to make it or if I need to hurry. Then I need to set an alarm for when work starts so I know if i'm running late or on time. If I'm watching a movie and I want to know what time it is I have to ignore my Watch and reach into my pocket to check. My watch will give me notifications but I still need to pull out my phone to check the time.
You're right that the time keeping component might not be the most important feature for some people, but removing it and making it optional doesn't make sense. What does Apple have to gain by doing this? What do customers have to gain?