This is a grammar problem rather than a math problem and grammatically the form "x(y)" is more useful if it is short hand for "(x * (y))" rather than "x * (y)". I don't think there's any situation where the latter would be more useful.

e: This video https://www.youtube.com/watch?v=lLCDca6dYpA has an alternative interpretation as to why it would be 1. 6/2(1+2) should be (6)/(2(1+2)) because if you wanted the PEMDAS compliant version you'd write 6(1+2)/2 so this shorthand makes sense. She finds many examples in textbooks and lectures that support this usage. One example was mn/rs being used for (n/s)(m/r) because if you wanted ((mn)/r)*s)) you would just mns/r which is much clearer. This isn't math; it's notation; and useful notation wins; PEDMAS is an oversimplification taught to school children. The formalization of this more useful rule is that multiplication by juxtaposition has a higher precedence than division.

This is a grammar problem rather than a math problem and grammatically the form "x(y)" is more useful if it is short hand for "(x * (y))" rather than "x * (y)". I don't think there's any situation where the latter would be more useful.

e: This video https://www.youtube.com/watch?v=lLCDca6dYpA has an alternative interpretation as to why it would be 1. 6/2(1+2) should be (6)/(2(1+2)) because if you wanted the PEMDAS compliant version you'd write 6(1+2)/2 so this shorthand makes sense. She finds many examples in textbooks and lectures that support this usage. One example was mn/rs being used for (n/s)(m/r) because if you wanted ((mn)/r)*s)) you would just mns/r which is much clearer. This isn't math; it's notation; and useful notation wins; PEDMAS is an oversimplification taught to school children.

This is a grammar problem rather than a math problem and grammatically the form "x(y)" is more useful if it is short hand for "(x * (y))" rather than "x * (y)". I don't think there's any situation where the latter would be more useful.