Yeah, if we'd designed around the case of explicit formal parameters we would have put them first. What we have is the endpoint of a series of design decisions not explicitly about that case.
PS In math other than lambda calculus it's also parameters first: f(x)=... or x ↦ ... But there are cases in which they come late, e.g., the result of a definite integral is sometimes shown as the result of the indefinite integral, then a vertical bar with x=a at the bottom right and b at the top.