Actually those are fine for lvalues. One can do for example the examples below.

x[2] = 7

(* Out[57]= 7 *)

x[11][5] = 4

(* Out[59]= 4 *)

Subscript[w, 2] = 6

(* Out[60]= 6 *)

The documentation for Set claims (first item in Details section) "lhs can be any expression, including a pattern". I don't know why that claim is made. If I am not mistaken, it is correct only in cases where the head of the left side expression does not have the Protected attribute set. That said, one can unprotect and remove that attribute (I do not recommend this unless you really know what you are doing though).

Look at the FullForm (if it is not clear already from visual inspection) You are attempting to assign, via Set, to an expression with Head of Power. But Set cannot do that because Power[a,b] is not a valid lvalue (that basically means it cannot be assigned to, in CS terminology).