Here is the problem with that line of thinking....there is no way for us to know.
I have been critical of Cook and some of his short comings as a player, but, I have never questioned his effort. There is no way I could know his effort. The concern about Robinson not approaching game prep as a pro was a real concern if it is still true....it may or may not be. We don't have a way of knowing.
In my opinion it is pretty unfair to assert a player isn't trying or doesn't care based on watching a few plays on a tv. A guy like Cook has some shortcomings as a player, but, he is playing against other players that are in the top portions of the top 1% of players in the sport. Any shortcomings are going to be exposed from time to time. A guy may use bad technique, may get sloppy with hand placement on a block or may lose the edge on a block for example because he is not quick or is being asked to execute something he does not excel at....it may look bad, but, it does not mean he is not trying.
Working with guys trying to improve their throwing velocity (pitchers) I have had the opportunity to see what pro guys do to work toward this end. Six to eight hours a day, five or six days a week would be the norm with the programming they were doing. That is what most people work in their day jobs of course. Nothing crazy about that. But, if you asked most people, even a lot in baseball, what do pitchers do in their offseason they would probably say, play catch and some jogging. In other words, appearances often dont mean much.
With a roster of 53 guys or whatever it is never going to be a group of 53 robots with the same work ethic, level of ability, free of personal problems, or even 53 guys that get along. It is just pretty unfair I think to single out a couple of players and basically say "this guy doesnt try"....like I said of the reporter asking about it, it is insulting really.
So what is the reporter supposed to do, it is great to talk about the players job, but the reporter also a has job.
Take Cook for example: So I guess the reporter could dance around it...but lets be honest those questions have been run through - why is Cook, paid like a top end TE not producing like it? Did you over value his abilities? (now we are questioning his talent is that allowed?) Does he have a health issue that is preventing him from producing equal to his pay? (now we imply the coaches are lying about his health status) Why can't the OC find ways to get him more involved and up his production? (now lets blame the coaches) Does he have focus issues, he drops lots of passes? (now we question his focus/ability/smarts)
The fact of the matter is that we all ask these question, and asking about effort is reasonable. It would be no different than no other shortcoming, maybe it is the players fault, maybe it is the coaches.
You say you can't know his effort...that is why the media, doing its job, is supposed to ask. They are supposed to get answers to such questions for the fans, because the rest of us don't get a chance to ask.
You say you work with pitchers...so take Rick Ankiel...should the media never ask if he was mentally broken? Would that be "insulting"? As a fan that is what appears to have happened, what was rumored at the time.
The signs pointed to a mental break (not a nervous breakdown, but an issue with performance pitching), I look at some of the players on the Rams and the signs point at effort, no I don't know, heck the coach likely never knows (cause what players comes to the sideline and says "my bad I half assed that"), but it reasonable to ask given the visual evidence.
That and honestly every professional athlete SHOULD know that a lack of on field performance can lead to that question.