IIRC, people have tried to create, and enforce, metric time in the past but it always fails. Basically it seems like that ever since the Mesopotamians invented base 60 mathematics for keeping track of time, some geometry, and related concepts it is stuck for that purpose because it really does seem to be the best number set for the job. It did not stick around for anything else though because it's basically garbage for those tasks. Base 10 works pretty good; it's easy to move around zeroes and decimal places, and since most people have 10 fingers it's pretty intuitive.

The use of base-60 for time and base-10 for most other things originates from different historical and mathematical practices. Base-60, or the sexagesimal system, is thought to have originated from the ancient Sumerians and Babylonians who used it for their astronomical calculations. This system has 12 divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, allowing it to be easily divided into halves, thirds, quarters, fifths, sixths, tenths, twelfths, and more, without resulting in fractions. This versatility has made it useful for timekeeping and angle measurement, both of which continue to be used to this day.

Conversely, the base-10 system, or decimal system, likely derives from the fact that humans have 10 fingers, making counting in this system intuitive and easy to learn. The base-10 system has fewer divisors: 1, 2, 5, 10, meaning it can only be cleanly divided by 2 and 5. While this system is less flexible for representing certain fractions, it’s more straightforward for counting and calculation, leading to its wide use in daily life, mathematics, and scientific calculations.

The integration of base-60 and base-10 systems hasn’t been widely adopted due to the significant societal change required. During the French Revolution, a decimal timekeeping system was attempted, with a day consisting of 10 hours, each hour containing 100 minutes, and each minute made up of 100 seconds. However, this system lacked popularity and was soon discarded.

Despite this, decimal watches exist today. These watches follow the concept of decimal time, dividing a 24-hour day differently, with an “hour” on a decimal watch being longer than a traditional hour, a “minute” being longer than a traditional minute, and a “second” being slightly shorter than a traditional second. They are typically seen as novelty or specialty items, appreciated by those who prefer the mathematical simplicity of a base-10 system. But due to the wide prevalence and deep entrenchment of the base-60 system in societal, technological, and legal systems, traditional timekeeping remains dominant.

(Source: I saw it on QI once - a British pub quiz style tv show)

I really want a decimal watch, just as a talking piece.

But I’m sure it would be a nightmare for actually keeping track of time.

You can blame the babalonians for that. They have a 60 base number system and was used for time and dates.

12 and 60 divide nicely. A quarter of a 12-hour clock is 3 hours, but in decimal time it'd be 2.5 hours. A third is 4 hours in base 12, but some gross 3.33 repeating in decimal.

I just don't like it.

Yeah, but honestly i think both are kinda stupid. we should use something sensible like base 16(easy conversion to binary but better readability) or base 12(easily divisible by 2, 3 and 4).

Decimal time was introduced in Revolutionary France, just like the metric system and a decimal calendar. They made it non-mandatory after 17 months, partly because of the enormous costs to replace all clocks. The decimal calendar survived longer and was abolished by Napoleon as part of his reconciliation strategy with the Catholic church.

Decimal time is still used by the way. Astronomers use fractional days because it's easier to do calculations with. And that very same ease of use is why Microsoft Excel uses fractional dates to calculate dates, as it requires less calculations.

Unix time is base 10 and I’d say it is pretty widely used. Not for wristwatches but by all kinds of software on the device you’re using to read this right now.