So what if we're on a different planet. The second does not need to change lengths. Whatever you change it to, the planets' days will still not line up, because you can't find a useful (or maybe at all) GCF of the rotations of every rock you decide to put something on. So your best option is to keep using the second, minute, and hour, because then at least you can speak of durations in the same way as people on the other planets.
Maybe for convenience, you could define a rotation unit for the planet you're on to speak of time of day when discussing with people on your planet. When dealing with anything not on your planet, you will need a standard calendar where absolute dates and times could be used. I don't see a date like "2345-06-07 08:09:10 Gregorian, local time 12.0000" as in any way problematic. It tells me the absolute date, allowing me to compare in nearly zero time whether this happened before or after some other event. Meanwhile, I know this occurred at midday, assuming they decide to stick with the concept of 24 sections of a day. If they don't want to do that, how about percentages for local time? That way, a planet with a long day will work perfectly well. 0% = midnight, 50% = noon.
And the second is perfectly defined using a seemingly random number of periods, because it is equal to the second we've been working with for a long time. Why redefine the second when almost nobody is actually using cesium to measure it? The people running atomic clocks can divide, while we can continue using all the standard second-based things we've used for a long time. Meanwhile, we've already limited this to running at sea level, so we can't avoid being arbitrary. For now, convenience. For later, simple utility. One arbitrary thing that prevents inefficiency is superior to two arbitrary things that require us to switch them. That's why we should stop changing our clocks twice a year.