The issue isn't so much the playing of bad vets. It's how we acquire them, and how many vets there are.
In the hypothetical alternate universe where we committed to a rebuild, and started trading some of our better veteran players for future assets, let's say instead of signing Staal, we traded Laughton and Walker to (random team) Vancouver for Tyler Myers, their #1 this year, and a prospect (pulling the name Podkolzin out of hammerspace here, I don't know who they value or how highly.) There's a perfectly serviceable bad vet, and now instead of Staal, Walker, and Laughton, we have Myers and space for Attard and Allison.
Then, if someone wants Myers at the deadline, we trade him, too, and bring up Ginning or w/e. It's better asset management, better player development, better process, and they still get their shitty vets.