I think it's because of a combination of a tight release schedule, limited budget, old coding from 2013 and too many packs to keep track of. They do not have the time to go through and play all the packs, once a feature have been greenlit, they are probably spending loads of time going through all the thousands of xml files to make sure that this new feature does not conflict with something else in the game.
I highly suspect the reason why they do not play the game, or go back and fix old bugs is because they are more focused on finishing it and are not getting rewarded for going back. They don't want to spend time playtesting the game, checking features, going back through thousands of xml files and fine tune them. They rather want to work on finishing their deadlines until the pack is finished.
There is a good story about the E3 presentation of Anthem, the devs was so rushed to put everything together that when they watched it at the E3 presentation, that was when they finally was able to see how it worked when all of it was put together.
