The Pulumi cloud offering provides state management.

With it, you can bring up some infrastructure on machine A and tear it down on another machine.

Without the service, you can only tear down on the same machine you brought it up. Ditto for adding to existing infrastructure.

You don't need their service but you have to solve problems like knowing what is running, replicating the needed state etc.

The service is very nice and makes it easy to know what is running, how long it has been running, who created it etc- across clouds. But, it is not strictly needed. As an individual user, you could get away without using. For a team, it fills a very vital gap.