It's an interesting one because anyone developing a software-only product has the opposite incentive - putting as much on the cloud as possible reduces support costs - no more "it says it's compatible with Windows, but doesn't run on my 20-year old laptop!" or having to field support requests from ancient versions. Plus it provides cover for charging users monthly, and there's a good chance your hosting costs are less than the cost of supporting a locally installed version.
The more complex your software is, the more true this is - self-hosted enterprise software is not only more work to setup (ergo, more support tickets) but installed on a vast array of configurations (e.g., bare-metal K8s, OpenShift, GKE, Docker Swarm, EC2, ECS, etc, etc), only a portion of which are economical to test against and which will generate a steady stream of unique issues. Having an "enterprise-ready" SaaS product is expensive, sure, but probably less expensive than supporting hundreds or thousands of customers setting up their own unique version of your product.
On the other side, it's not possible to move hardware to the cloud so the core support costs don't - can't - go away. Adding cloud in that case is adding ongoing hosting costs and support costs and is at best reducing the volume of support requests, but adding "Cloud" won't eliminate whole classes of customer support like it could with a software-only product.