Of course, theoretically you could also view the function as a parameter of the computation and/or the arguments as specifying an operation (in particular if those are also functions), but for most concrete function invocation that's not generally the mental model. E.g. in "sin(x)" one usually has in mind to compute the sine, and x is the input for that computation. One doesn't think "I want to do x, and `sin` is the input of that operation I want to do". One also doesn't think "I want to do computation, and `sin` and `x` are inputs for that computation". It's why you may have mentally a sine graph ranging over different x values, but you don't imagine an x graph ranging over different functions you could apply to x.
Incidentally, that’s also why we use syntax highlighting. One could, of course, use syntax highlighting instead of symbols to indicate the difference between function and arguments (between operation and operands), but that would interfere with the use of syntax highlighting for token categories (e.g. for literals of different types).
The drawback is that they are put on the same level, whereas in most people’s minds the function is a fundamentally different thing from the argument(s). The “f(x)” syntax reflects that asymmetry.