Why is the multi-step reduction of semantics reflexive?
The practical reason is that it is very convenient to include also the case "zero steps" in the definition of "many steps" (millennia of mathematical experience have taught us that it is usually a good thing to have a 0 around in our set of natural numbers).

One possible technical exemplification of this (but there are probably dozens more, perhaps more interesting than this one) is that $\to^+$, the transitive closure of reduction, does not satisfy the diamond property  (a.k.a. confluence), whereas $\to^\ast$ satisfies it.  For example, if $I:=\lambda x.x$, there is no way to close the following critical pair by means of $\to^+$:

$$I \leftarrow (\lambda x.I)(II) \to (\lambda x.I)I$$

To close the span, you need to consider the empty reduction $I\to^\ast I$.