Does anybody manages a private IT cloud within a business that also uses public cloud (ie. multi-cloud strategy). Have you managed to promote the use of the private cloud alongside the hyperscaler offering?  Are there services you've managed to offer to your business via private cloud that means the investment you've made is utilised rather than devs and users just defaulting to public for everything?

When you focus on multi-cloud strategy, it is important to define and document that strategy part: what cloud environments do you use, and what is their purpose/positioning? Do you constraint specific applications or services based on their non-functional requirements or security/compliance requirements?

In our environment, we have both on-premise as well as two strategic public cloud environments. However, for the public cloud environments we do not position traditional workload on IaaS - for that, we have on-premise, as this is in our case much more integrated and worked out from management & support services PoV which would need to be completely revisited if we were to focus on IaaS in the public cloud as well. Instead, we focus on the platform services of these public clouds. Furthermore, depending on the criticality, data gravity, and other considerations, some public clouds might or might not be used for workload. 

Vice-versa, we have certain application development lifecycle choices where we clearly identify a single public cloud as the target hosting (and not on-premise anymore). It all depends on the purpose of the workload, the data that is used, and the non-functional requirements that need to be fulfilled.

In Brasil´s Correios, we only use private cloud for our production applications. VMWare with the remaining non new licences. Soon we´re going to migrate to subscription. Still we keep the workload on private cloud to minimise public cloud costs. Once we had one of our workloads tested in production on GCP and AWS. The billing made up our minds. We are going to keep it on premisses as long as we can. But of course, we have an on premisses culture that allows this kind of savings. And yes, our datalake is migrating to AWS. It was on GCP.