Agreed, we can do that, and it is done for many kinds of circuits. But many others don't work like that, so it's wrong to say that hardware works exclusively like this.

One other common pattern for implementing conditional logic is to compute a boolean expression in which the control signal is just another input variable. In that model, to compute Y ? foo(X) : bar(X), we actually compute baz(X, Y) whose result is the same. This is very commonly how ALUs work.

And the other very common pattern is to split this in multiple clock cycles and use registers for intermediate results. If you don't have two circuits A and B, only one circuit that can compute either A or B based on a control signal (such as simple processors with a single ALU), this is the only option: you take one clock cycle to put Y in a register, and in the next clock cycle you feed both Y and X into your single circuit which will now compute either A or B.