Only if we also incorporate units of time that are also divisible by 10, and get rid of this seconds/minutes/hours nonsense.
I'd support this.
Why? In some significant respects base 60 is superior to base 10. Also there's nothing preventing you from using kiloseconds (16⅔ min) or megaseconds (11.5[740] days) if you want to. It's not something I'd want to pick up since I'm already halfway thru my second gigasecond.
Indeed, base 12 is very mathematically superior to base 10, so base 60 works well too as 12 is a divisor of it.