Why does German prefer the ordinal century names (18tes Jahrhundert/18th century) and almost never uses cardinal numbers (1700er [Siebzehnhunderter]/1700s [seventeen hundreds])?
Why do horses have four legs? Why do firs have needles instead of normal leafs? Why does Hungarian language have 31 cases? Why is there no declension in Japanese language?
So many questions, all with the same answer:
It just happened.
Languages are things that evolve over the time, like animals and plants. And languages follow the laws of evolution like creatures: There are many small changes over the time, populations are split when spreading across geographic regions, and when they are separated, they develop in different directions.
The special feature, you are talking about just didn't develop in German, but it did in English. For no special reason. Just by accident.
There is actually a slight difference between the two. In my head, im 18. Jahrhundert tells me something happened between 1701 and 1800, while in den 1700ern tells me something happened between 1700 and 1709.
So the hunderter-variant makes me think more of a decade while the century of course talks about the entire century.
Other than that, the answer is, of course, ‘it evolved that way.’