Separate SQL Logins for reading from and writing to table good design?
You simply need to follow the Principle of Least Privilege.

If you have one entity, whether it be a user or an application, that entity should have an account with the minimum permissions required to do its work.  So if you will have a web API that will only read from one table, then its website should be using an account that only has permission to read that one table.

Your question doesn't seem to indicate who or what will be using the read/write account.  If nobody will be writing to the table (which I'm guessing is correct, based on the fact that the data came from another source), then only the ETL process should have permission to write to the table.