It’s not a limitation but a matter of precision. The position of the minute hand tells you how far into that minute you are. You don’t need that information, of course. You can just say whatever mark it’s closest to. At 1:00:58, although a digital clock would still read 1:00, it is by all accounts much more accurate to round the minute to 1:01.

So if you just call the time by the minute your minute hand appears closest to, you’ll often be more accurate than a digital clock. It won’t matter. But you’ll know it’s true.