Earlier quoted context omitted.
Totally agree with all your points except >there's not a lot of empirical evidence to support claims that automated tests will improve developer productivity or code quality. If you'd have said "there aren't any published papers _proving_ this" I would've agreed simply because I do not know if such studies exist or not (they might); but I'd argue that automated tests obviously improve code quality and productivity. A…
Generally speaking "empirical evidence" means "published papers", with a little bit of flex for preprints or trustworthy-but-not-peer-reviewed experimental findings.
The subject of programmer productivity is both much-studied and discussed and very hard to define, measure, and compare. The studies that do have some empirical evidence seem to show that team dynamics and individual programmer personalities have the most dramatic effects, compared to things like programming language, tests, style guides, etc. It's not that consistent styles and automated testing are bad ideas, it's that they don't clearly make a big dent in team productivity in cases where one or a few incompetent (or merely slow) programmers, or one jerk, can derail everyone's productivity.
This I why I emphasized demonstrating a commitment to the team and showing some contributions before criticizing the environment and trying to propose changes. If you want the project to grind to a halt tell your new co-workers they are doing everything wrong. No automated test suite is going to fix that problem.