What I don't understand is why the most literal translation into English, which is equally succinct, doesn't "work" somehow. Namely the translation: "hurry slowly".

It's just so awkward. Yet the grammar isn't bad; there is nothing wrong with "walk slowly" or "eat slowly".

"Ponáhľaj sa pomaly" is perfectly euphonic to the Slovak ear, while "hurry slowly" seems clumsy somehow. We need to make it more sophisticated somehow, like "make slow haste", or "slow haste makes faster" or whatever.

What is the reason ...

I suppose; if everyone said "hurry slowly!" it might wear into usage.