Since LinkedIn shut off their contacts APIs, folks have been looking for other ways to get at LinkedIn connections data. Export is an obvious solution - even though it requires some friction on the part of the end user, people are often willing to jump through a couple hoops if your app solves a real pain they have. By increasing the friction, people developing apps which try to make use of LinkedIn data have to try harder and inflict more friction on their users, hopefully (in LinkedIn's eyes) shutting down more of those apps for good.

One optimistic possibility is so that if you leave your LinkedIn account logged in on a computer somewhere, another individual can't immediately export all your contacts, which could have competitive or security implications. It takes multiple days and you get notification of it happening.

"What purpose would this serve?"

Lock-in is the only answer that makes any kind of rational sense. The harder you make it to get your data out of any software/website the more friction you add to people who may want to try alternatives.