LinkedIn has different kind of users. In a simple way you can say it’s “people who want to find others” and “people who want to be found.”
By looking at each users needs they realized that it’s in everyone’s best interest, including LinkedIn’s, to have users with complete profiles. So they designed their search feature to include profile completeness as a metric.
If users want to be “found,” they need to fill in everything. Those “looking” then have more complete information at their hands, and LinkedIn is more useful to both as a result.