What is a sense of Power BI Report Server if we already have Power BI Service? I understand that Report Server is on-premises solution and PBI Service is cloud based. But in each case we can connect selected users to interact with our saved content. So why do we even need Report Server? Are these deployment modes so significant?
MS want everyone to move to the cloud. The on premise server is something I suspect they've undertaken reluctantly as too many companies just won't push thier sensitive financial data into the cloud, so PBI service take up was blocked in some of the bigger commercial clients and certain industrial segments. So Microsoft are trying to make sure these clients have somehting to tide them over until they're either comfortable moving this kind of data to the cloud or the regulation and legal framework around data sovereignty becomes clearer as existing cntracts take account of the new legal landscape. That and maybe they can offer a "good enough" on premise solution.
Data sovereignty is going to become a much bigger issue than it currently is and its already an issue that cloud vendors ignore (or gloss over) at their peril. Until MS provide bring your own key capability (not currently supported for PowerBI as far as I am aware) there are whole swathes of various industries (law and healthcare in the UK and EU for example) that just can't put their data in the cloud as they can't actually provide the kind of legal/contractual commitments to data security and access that thier clients or regulatory oblligations require. Doing so right now means you are placing your trust in the US legal system to not just grant access via a court order in an extra-jurisdictional fashion. If you're in the EU that has the potential to put you in an interesting position should someone in the US decide to go grab your data because MS is a US company and US law is applied even to its data centres around the world in other legal jurisdictions.
Who owns the data, where it "resides" and which set of jurisdictional legal undertakings apply to it are going to be interesting questions of the next X years, most of these are currently untested.
Like many others, keeping our data on premise and within our security perimiter is a contractual requirement so unfortunately the cloud isn't an option. So the on premise server is where its at for us, or we go buy somehting non Microsoft.