it doesn't matter whether your 4 is a birdie or a par. its still a 4.
Pinehurst #4, a par 4 on paper, is really a par 5. Pinehurst #5 which is labeled a par 5 is actually easier.
A club I used to belong to, the opening hole was a par 5. When they did USGA qualifying there (3x, twice for regular, once for seniors), they called it par 4. So what.
The point is score. 4 is 4 no matter the label.