In a hybrid-cloud context, is it reasonable to use a tool in a public-cloud to analyze data stored in a private cloud?

It's not only reasonable but quite common to use tools in a public cloud environment to analyze data stored in a private cloud within a hybrid-cloud setup. Hybrid cloud architectures are designed to leverage the advantages of both private and public cloud environments, allowing organizations to maintain control over sensitive data and critical workloads in a private cloud while taking advantage of the scalability and flexibility offered by public cloud services for tasks like analysis, processing, or applications that may have variable resource requirements.

Considering the background as I posted earlier, I think it's not reasonable to use public-cloud to analyze private clod data for enterprise and large-scale use.  Difficulty of managing interconnection overhead and access control include data traffic, access control, data protection, synchronization with IAM and so-on.   

There are some specific use cases, such as patent analysis, legal affairs, pharmaceutical affairs, etc., where there is an analysis source on the external service side, and it is combined with that and analyzed by matching specific information in internal data.

In this case, we may perform limited data linkage directly with a public cloud that has that specific function.

At that time, instead of linking all data, the design may be such that only the data to be analyzed is linked upon request.

I think this depends on the amount of data handled and the scope of the information, but considering traffic and response, it is often better to place data and tools in a close environment. When handling small-scale data in a specific area using SaaS, data analysis from a nearby public cloud may be used. Basically, generated data is often aggregated into IaaS or PaaS close to the company and used for analysis. Data lake creation in Azure is one example.

From a different perspective, when performing data analysis in the public cloud, it is often necessary to separate data access rights and protection by data type, customer data unit, confidentiality level, etc. In that case, linking internal role management such as IAM with public cloud tools is often complicated or impossible.

Due to the above background, when performing data analysis in the public cloud, the data area is often narrowed down to a specific task.

From an I&O perspective, you may want to narrow down the variations of management tools as much as possible.  Recently, instead of adopting a separate public cloud environment for analysis, we are gradually consolidating into an environment where authority management and data management can be unified in collaboration with IAM. Microsoft and SAP families fall under this category.

From a maintenance and management perspective, there is an intention to migrate the historical on-premises data analysis system to the cloud.
We are gradually working on this, but converting custom reports with a large number of users or historical custom reports is a challenge.
We are moving forward with the migration of our server environment to IaaS, but each time the version support deadline comes up every few years, we are wondering how long we can continue to operate our own servers, including IaaS.

This is a topic of inter-cloud architecture