That's correct, and as you illustrate it's the possibility to have newlines and commas inside quoted fields that complicates things for grep/awk/cut/etc.

So instead of making a more complex version of tools like grep, we can make the data simple for these tools to understand. That's what https://github.com/dbro/csvquote does. It can be run in a pipeline before the grep stage, and allow grep/cut/awk/... to work with unambiguous field and record delimiters. Then it can restore the newlines and commas inside the quoted fields at the end of the pipeline.