If I was a developer there, I'd totally started adding those generated tests. I have a job to do (ship products) and you put in some stupid requirements which actually interfere with it (since my time is limited I can either work on tests or my daily tasks like developing new features or fixing bugs), but we both know that if my primary job suffers, I'll pay for it. So the best solution, from my point of view, is the one that takes that requirement away and lets me go on actually working.
When we had a similar problem in a previous company, we just created an epic, assigned a couple of people to it and have them churning out tickets for specific improvements, like "Class X has a coverage of Y on this method, add tests for the missing execution branches", which were clear, non-generic and fully integrated in our flow. If anybody complained about our velocity or whatever, we could show them the full trail which lead us to choose to work on that ticket and how much we spent on it. The coverage issue got solved in less than a month.