Hours, minutes, seconds, AM, PM, Noon, etc. are based on solar time, otherwise known as sundial time. Though it continues after sundown. Standard time is based on the mean solar day. I don't understand it myself. But each solar day is not exactly the same. Each solar day is a couple of minutes faster or slower than the previous and one that follows. This is called sunfast. The reason we use the terms AM, PM, Noon is because that system was most familiar to people at the time, when Standard time started in the US in the 1880's. Of course Daylight time is something even different from that. Standard time is based on Noon, when the Sun is in the center of the sky. Even though it's the earth, not the Sun that is moving. But for the sake of time, sundial and Standard, we assume that the Sun is moving. Just like the ancients would have. In the military, they use a 20 hour clock. Twelve hundred hours, thirteen hundred hours, etc. They use this system in airports too. And it is better, because it doesn't change over from AM to PM like we still do. They did try a decimal clock in France during their revolution. Each day was divided into 20 hours, 10 for day and 10 for night. Each hour was divided into one hundred decimal minutes and each minute one hundred seconds. But it failed because people found it too confusing. Plus it probably didn't help most people back then were illiterate. Some people think though that the world should all switch over to the military system. That would be the best option for the reasons I just gave.
I think we should all use the current star date. Right now it's -298622.95. So if you need to know the current time, you can find it here: Stardate Calculator
The reason I would not agree with the base 10 system is that nothing can be divided by 3 or 6 without a recurring decimal. The same is true for measurements used in engineering and causes endless problems.