If stardates are arbitrary out-of-universe, they should at least be extremely complex in-universe, since those human(oid)s see what we see; they must need the ship's computer to help them out.
Also, the fact is that they aren't being confused by any time issues on a regular basis. Five days on the ship is five days on a starbase; calendar years in space aren't different from those on Earth. The writers need that simplicity. The humans are probably using our Gregorian calendar to determine that an event occurred "two months ago", whereas stardates are recorded in logs and official files. Other Federation members might be employing their own planetary calendars, with the universal translator taking care of conversions.