Should people be searchable by default on digital platforms?

I've been thinking quite a bit about privacy while working on a software platform.

Most platforms make it easy to search for people and connect with them. But should that really be the default?

We're exploring an approach where users decide whether their profile can be found or stays private. Connections would also require an invitation rather than just clicking a button.

I'm curious about people's actual experiences.

Have you ever wanted to keep your profile private on a platform but found it difficult to control who could find you? What did you do?