Much as I love the metric system, I kinda think the moment for changing time units has passed. At the latest when computers became a thing, probably even before that.
And 12 based systems have the advantage of having having many divisors which is very neat as well. You can divide an hour by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 and end up with an even number of minutes. Then again with a decimal system fractions wouldn't be so bad.
I'd prefer base 12, but with given the current state of numeric affairs I'd much prefer metric time over using metric for everything except time (and screen diagonals)
That way, with decimal time, large scale planning becomes much easier to grasp. This part of the project takes 3.475 days (=3 days, 4 hours and 75 minutes), 200€/h from the customer makes that part days × 2000€ = 6950€...
(and that way I'd just know my laptop's screen size is 40cm instead of it being marketed as 15.6 Unicorn units while actually being closer to 15.75🦄)
I'd prefer if it already was decimal time. As you said it would integrate with the rest of the metric system much more smoothly.
But as a software developer the thought of changing it now gives me anxiety. Time is so much more immediately integrated into systems than distances or currencies.
While I do understand the better divisibility of base 12 and base 60 providing more whole numbers, I don't know if it really helps anything. 1/6 of 12 is 2 and 1/6 of 10 is 1.666, so on paper, 12 looks clean. But I can't really gauge dividing something into 1/6 physically any better than if I just try to fill 6 pots equally. Did it really take that long for decimals to be invented?
The again, it's too late in the afternoon for me to do 10/6 so I used a calculator. I guess it does help.
Dividing things neatly appeals to some part of the human brain that appreciates order and structures. There’s a certain type of beauty in it. However, when you’re actually measuring, cutting and building stuff, you end up with really messy values, as you are dealing with harsh reality instead of some ideal fantasy.