Would UPS and FedEx be in a good position to become bitcoin escrow services?
Yep. You can use your imagination to see what will happen with their position. Their profits maybe won't get a way higher, but they will become very popular.
They are already popular. Even more so when you consider the fact that USPS has a monopoly on being able to use mailboxes that are attacked to every house in the US.
A company generally does not care about how "popular" it is, their main concern is their overall profits, so if their profits will not increase then they will likely not enter into this business.