I think I remember playing around with an early attempt at handling data within SSDT projects and it wasn't quite intuitive. Post-Deploy and MERGE type statements do work, especially with some sort of temp table or such to compare against, but it's not an easy problem to handle. We see some of that done within the "bacpac" structure, but that's a full on "this data should be there" and doesn't necessarily take into account cases where you might have a mixture of data. I know some systems have a "system-required" set of data as well as a "user-entered" set of data. You _need_ the system data, but you can't completely replace the table's data with it because there's that set of user data as well.
For our purpose, the post-deploy scripts have worked pretty well, but we haven't had to handle a large number of records/tables. If we had a large number of tables to maintain, we'd probably be looking at some other solution that could better handle comparing a static set of data with the data in the table and update it to match. Red-Gate has an advantage here with Data Compare, but MS could likely do something along those lines with its limited data compare in SSDT. Either way, if someone added new columns with required data, you'd need to manage that dataset.