You are absolutely right. However, the missing DLL's are part of the MSFT 2008R2 operating system, which means that our predecessor never evaluated the chance future operating systems might work differently. We have a workaround for that problem , though. The challenge seems to be to get the proper installation of tooling to perform the update in the first place..
So the problem, in truth, has nothing to do with SQL Server nor SSIS, and specifically that the package(s) are using features that the operating system (Windows in this case) no longer provides or works differently. That should be and is an expectation that you should have when updating the underlying operating system.
This feels like what you are effectively asking isn't "how do I not upgrade the packagesfrom migrating from SQL Server 2008 to SQL Server 2016" but "How do I upgrade the packages, but get them to use deprecated/removed features of Windows 2008 on Windows 2016?" For that, you need to update your packages to use the new standards, much like you would with any upgrade path.
Excuse my typos and sometimes awful grammar. My fingers work faster than my brain does.