✗ "pay the drinks"
in English either, even though you can
○ "pay the bill"
○ "pay the rent"
○ "pay attention"
In other words, 「〜を払う」 corresponds more closely to "to pay ~" than "to pay for ~", which should not be surprising considering that is the syntactic equivalent.
As to why Japanese uses 「〜のお金を払う」 instead of 「〜に払う」 (i.e., an indirect object) to express "paying for" something...
In English there are a ton of uses for "for": 32 according to the Random House Dictionary. The relevant one here is categorized as
8. in consideration or payment of; in return for: three for a dollar; to be thanked for one's efforts.
While some of the uses in that dictionary entry are accomplished by 「〜に」 in Japanese, certainly not all of them are, including this one. You often need more complex expressions like 「〜を目的として」、「〜のための」、「〜に関して」, etc., and this is one of those cases. Prepositions/postpositions are often extremely overloaded in languages, and they evolve over time by people using them for related-but-slightly-different purposes, naturally allowing for extremely branched meanings in different languages.