Or, if the programming language uses infix binary operators:

Not if the programming language has evaluation order from left to right, e.g.

2+3*4

is evaluated as

(2+3)*4.

For example J uses this kind of evaluation.

J is APL-inspired, and APL is right-associative, so that would surprise me. https://www.jsoftware.com/help/jforc/preliminaries.htm#_Toc1... agrees with that, saying

“All J verbs (functions and operators) have the same priority and associate right-to-left. For example, a b + c is equivalent to a * (b + c), not (a * b) + c.”*

Your point about not needing operator precedence still stands, though.

Smalltalk also.