It's useful if the value of b is actually the result of a function call that has side-effects. In this situation you may want the function to be evaluated even if the resulting expression is false (because the value of a is false). I do agree that the alternative syntax is not intuitive though.

What exactly is the purpose of having two different ways of using (a && b), one with and one without lazy eval.

The point of having both lazy and eager evaluation is that they are different.

The way the current compiler works, it is not possible to for example

a || b

to stop evaluation if a is true, but

a || {b}

scope with b will be ignored, unless a is false. Ideally it would have benefited to have lazy eval all the time, unfortunately not possible with current compiler.