Quite important, actually. Day and night cycles determine when solar power is available. You'll probably have some outdoor activity by humans (mining, construction, maintenance, etc...) that would be affected by daylight. (Perhaps most work will actually be done at night to avoid radiation from the sun?) And even in a hardened habitat you might have skylights (maybe long tubes or solar collectors connected to fiber optic cables rather than big windows in the ceiling).

> The fact is that modern societies don't really need a calendar synchronised to the seasons. Most jobs nowadays the seasons are not very important.

I work an indoor job, but still the seasons affect me quite a lot. (It's cold and rainy in the winter.) I don't know what the seasons are like on Mars, but I could imagine outdoor seasonal differences in temperature and light levels could have some impact on colony logistics.

> For the first few decades at the very least, Martian colonies will be dealing with Earth an awful lot.

Sure, but if the lead time between ordering a part and receiving delivery is something like six months or a year, it's probably hard to care that much about what's going on on Earth in real time. Sort of like someone who runs a business that buys parts from vendors in China is probably aware of the Chinese New Year. But that doesn't mean they run their life primarily off of the traditional Chinese calendar.

> I don't know why you'd do that. On earth, clocks run from 00:00:00 to 23:59:59 each day. On Mars, you'd just make them run to 24:39:34 instead.

Well, sure, that's the practical solution. But it's less poetic than having some interval every day where the accounting of time is put on hold.