Yes, there is. I would absolutely think differently if given convincing evidence that managers have a strong impact.
All I need is two things:
1) a repeatable measure of managerial impact that shows year to year correlation.
You know how I know (mathematically, not intuitively) hitting home runs is a skill? Because if I split players into two groups, "good at hrs this year" and "bad at hrs this year", then historically it is overwhelmingly likely that the "good" group will be good at it next year. Even if they switch home parks or managers or get older, the skill persists.
You wanna assert that a manager is responsible for the difference between his team's war and their records? Sure, that's a hypothesis. And it's one that's *really* easy to test. Split the managers up into good/bad groups each year throughout history and see if the good/bad groups persist.
This isn't some incredibly esoteric and hard to measure voodoo. Sabr mastered this horsefeathers 50 years ago.
Once you have that correlation, you've gone most of the way to changing my mind. All you need now is
2) a compelling, logical reason why the highly analytic, extremely dollar-efficiency obsessed world of modern front offices isn't taking advantage of this gigantic market inefficiency. A marginal win still costs about $10m on the open market last I checked. A 10-win swing should be a $100m value going for a marginal investment of a few million dollars per year.
If those two things existed, I would *absolutely* believe that managers have a large impact.