Hi Essah, I'm a native Brit, and it sounds more like an older way of speaking (if you directly translate) e.g. in the past someone might have asked 'what is the hour', in which case, the reply may have been in the ordinal 'it's the third hour' Modern English is different (i.e. what time is it). There are other cases of this in Czech, especially with sentence structure e.g. 'nejim maso', old english; 'I eat not meat' modern english; 'I dont eat meat'.
You just have to imagine like you're in a period drama.
I guess the real question is why then does one not say půl první as well. Why is the language inconsistent about whether a cardinal or ordinal is used?
Czech appears to be the same as German in that they are saying half an hour to (two in this example.)
It is initially confusing for Brits / other English speakers. I always arrange to meet a German person on the hour, not on the half hour. It avoids someone being an hour early or an hour late for that meeting !