It may be confusing for a newcomer (or on first read-through) that the variable/predicate/condition that represents the "necessary condition" in this statement P ⇒ Q is the Q.

One might be forgiven for incorrectly assuming that the P represents the necessary condition. That is because most of the time when one states a statement/relation/implication/etc. about a subject, the sentence/statement begins with the subject. For example, if we're explaining about a "less than" relationship, and we give x < y as an example, one would correctly assume that x is the subject here and x is the thing that is less than.

So it may be a bit surprising to a newcomer (on first read-through) that the subject of this section — the necessary condition — is represented by the Q and not be the P.

(Made even more confusing by the fact that the very same implication P ⇒ Q is also used to express the opposite sufficiency relationship in the very next section. I would argue that Q ⇒ P should have been used instead in exactly one of these sections to make it clearer that the subject is different and/or the relation is different, depending how you look at it.)

Is there any reason we couldn't rewrite this to express the logical relation between P and Q with the subject first? If we let P be the subject (that is, "necessary condition" that we're illustrating/explaining), could we not rewrite this as P ⇐ Q?

In fact, that is exactly how this relation was expressed below, in https://en.wikipedia.org/wiki/Necessity_and_sufficiency#Simultaneous_necessity_and_sufficiency !:

that P is necessary for Q, P ⇐ Q, and that P is sufficient for Q, P ⇒ Q