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Nice job, Doc.
I'll give you my feeling on why managers (as a group) prefer "set roles" - and why this "may" actually be a benefit.
In short -- "set roles" simplifies the managers' job. While baseball may seem simple to the casual fan, anyone who has followed the game at length understands that there are dozens (if not hundreds) of variables changing from batter to batter (or pitch to pitch). The BEST managers are the ones who are thinking 3 moves ahead -- where the wrong decision at this moment has the potential to induce 3 even worse moves behind it.
As a chess player, you obviously understand the importance of getting everything you CAN take care of *BEFORE* the match out of the way -- learning the openings, the variations, the game theory -- that you do on YOUR time. When the game begins, a LOT of your analysis is done before the first move. You then attempt to employ it optimally -- which means following your pre-game plans and strategies TO A POINT.
Having "set roles" allows the manager to consider the "typical" patterns of ebb and flow and performance, and have a really good idea of what to do without the need to think it thru in the 30 seconds he has to make the critical decision with 2 on in the 6th. There is, of course, room for instinct and variation from the standard in some cases.
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Why I think this may actually be beneficial. Because PEOPLE tend to like stability. While individual personalities may vary, imagine having a job at a car dealership, where any day you go to work, your boss could choose to RANDOMLY assign your job for the day. Monday: Salesman -- Tuesday: Service Desk -- Wednesday: Shuttle driver -- Thursday: Loan Approvals -- Friday: Shipping & Receiving. It doesn't matter if you are equally adept (or inept) at each job -- the very idea of having no idea what you are going to be doing on a given day - for most people - is going to be draining.
Of course, there are personality types who may thrive under such a situation. But, by and large, most people would prefer becoming truly proficient in ONE thing over being mediocre in a bunch. While being a middle reliever or a closer may not be as different as Salesman and Shipping Clerk - I believe the concept is still valid. The very fact that we are discussing different situations sort of proves the point.
I recently brought up Boston's first attempt to employ the Bill James' "best man for the job at the moment" bullpen utilization plan, which largely failed. The counterpoint from many of the sabre crowd was that it didn't fail due to the deployment plan - it failed because the bullpen simply didn't have enough talent. There may be some truth in that - unless you open the door to the possiblity that the utilization plan may have actually contributed to the players in question performing UNDER their talent levels.
A manager's job -- ANY manager, baseball or otherwise, should be to maximize the potential of all of his staff to their fullest. If knowing what your job is going to be when you go to work makes you more comfortable, (and therefore more productive), why should the same not be true of the bullpen arms?
I know of no way to study this objectively. But I have heard anecdotal evidence -- where a pitcher "understood" his role to be "X" -- and on a random day, the manager decided to use him in role "Y". The surprise of the change completely threw the pitcher off his game and he got shelled. It was a purely mental issue -- just like the quiet guy in the back of the weekly meeting -- if the boss says out of the blue - "Joe, we're gonna let you do the presentation today," with no warning -- you're likely going to be watching a train wreck.