The ESV Study Bible says that the regulation concerning entrance and exit of the temple courts may be merely for crowd control, but suggests that it probably has some deeper significance. My guess is that the LORD is telling us that once we have approached his presence in worship, we should not turn back to the way things were. His presence and grace should change us.
The only exception to this rule is the prince. If he represents the Messiah, it makes sense that he is an exception. Worship changes us, but not the Lord.
LORD, forgive us for coming to you in worship, then constantly going back to our normal lives. Change us, and make us exit your presence a different way.
Ezekiel 46