Is moving data storage from on-prem to public cloud always cost effective?

One of the major benefits when switching from on-prem to cloud storage infrastructure is the relative ease with which data can be moved from rapid-access to longer-term storage. Especially when data has to be retained indefinitely for proof-of-purchase purposes there is no need to have the data online. It is fine for most use cases for there to be a delay in retrieval. We find that the cost of such storage can reduce the expenditure in that category by 90% or more. Additionally we find some (but not all) online storage providers very capable in cost-effectively moving large amounts of data from off-line to on-line and vice versa. What has surprised us on a number of occasions is the cost and time-delay in moving / uploading data from on-premise to the cloud: if that is part of your future plans, look at ways to physically ship drives instead of uploading data. 

It can be if you weight all factors properly and go with the proper provider and options that work for your use case.  When migrating to the cloud you have to consider data availability, transaction frequency, scalability, security, compliance, etc.  It is imperative that you understand how you intend to use the data you will be moving to the cloud so you can make the proper decisions that will be most cost effective for your scenario.

It all depends on how much data is there. For small firms with a limited amount and type of data, local storage is probably more effective and costs less. For large enterprise with a lot of xompelx data, it willd efintely save the cost. 

Not always, but generally yes, if planned right. This depends on a lot of factors:
1. How are you storing your data locally. Are you using a Database, which one? Are you storing in a data warehouse? which one?
2. How are you planning to store the data in Cloud?
3. How much quantity of data do you need as "readily available" and what rest can be "archived" on less costly storage solutions (eg: AWS S3 Glacier, similar to Azure Blog Storage and GCP)

In general, if you have an SME guiding you, and you plan right, and keep cost savings an equally important KPI in the metrics you track to mark the project as successful.

PS: All major cloud providers will be very happy to provide you one free of cost, and even "fund" your migration activity and give you joining "credits" to make sure you become comfortable with their cloud offerings

Things that I feel should be taken care while taking decisions related to data storage:
- Volume of transactional data being generated everyday
- Archival policy as per the business needs 
- Identification of read path and write paths basis the traffic in the systems and interdependencies
-  Absolute volume of your data in your warehouses
- Growth curve of the data in both transactional and warehousing systems
- Privacy of data if is a major factor then the straight away answer is "on perm"

Basis the above factors, you take calls 
- The tools/tech stack that would be required to solve above problems
- Time taken to build the on perm capability vs cost of it to the business
- Cost effectiveness of having on prem vs cloud
- Infra and operational cost for both the options