Why is answer A (遊べるために) wrong in this question?

Question

この公園には[a. 子供が遊べる/b. 子供が遊ぶ]ために、ブランコが設置してある。

I thought of "A swing is installed in order for children to be able to play in this park", but apparently that's wrong but I can't figure out why.

I see why B is correct but I don't get why A would be wrong.

Answer 1

子供が遊べるために sounds awkward to me. I think we usually say:

• potential form + ように
• plain form + ために

to mean "so that ~~ can do ~~" / "for the purpose of ~~".

So in your example I think you could say:

• 子供が遊べるように (lit. so that children can play with it)
• 子供が遊ぶために (lit. for children to play with it)

Some examples:

• [東大]{とうだい}に[入]{はい}れるように[一生懸命]{いっしょうけんめい}[勉強]{べんきょう}する。
  (I'll study hard so that I can enter Tokyo University.)
• 東大に入るために一生懸命勉強する。
  (I'll study hard in order to enter Tokyo University.)

Answer 2

I agree with you. A seems to be as good as B.
The only detail I can think of is one of logic, not grammar.
If the swing is there so children CAN play, does it mean that children CANNOT play without the swing? That is not true. Children can still play even without the swing.
If you say 子供が遊べる, it means that children cannot play without the swing, which is not true.