I think your suggestion works well at a smaller company (<50 employees), but as the company starts moving to multiple floors/buildings and departments become a bit more isolated then the organic lunches tend to be intra-department vs inter-department. We have lunch brought in once a week. On the days we don't have lunch it is very much as you describe within each department, but on the day the company provides lunch it is very common to see engineers eating with the account management team and that is when the useful conversations happen.
I don't know, This is more or less how my company works (~150 people). It scales well, because even in a larger company there is a certain amount of intermingling between teams as developers change roles over time. For example, I know a lot of people in my company because I have moved across several different teams during my four year tenure. I just throw the people I want to hang out with at lunch on a Skype group chat. Sometimes they join and sometimes they do not.
On a different note, at my company, talking about work at lunch is pretty taboo unless the topic of the lunch was previously disclosed by the initiator to be work-related. Lunch is when we talk about all kinds of other bullshit and only talk about work if we're desperately spinning our wheels on something or want to vent.
That sounds like some form of confirmation bias. You may not be aware of the usefulness of conversations that happen under circumstances not favorable to you observing their content.
The company-supplied lunches lead to useful conversations in a place where you are able to judge their utility.
When people from your office go out and do not invite you, you are unable to know who is talking to whom, or what they are talking about. And you should not know, because that would make you a spying creep.
Confirmation bias is fine here, because we are trying to establish whether or not lunch being provided benefits employees. The anecdotal evidence suggests that it is beneficial to >0 employees at >0 companies, therefore the claim that it only benefits the employer is false.
You also have to show that it could not have been more beneficial for the employee to be doing something else.
You can't discount opportunity costs. If Oprah was giving away cars to everyone who went out to eat lunch at a local strip mall, you can't reasonably say that a person who found a quarter on the break room floor benefited by staying in the office to eat lunch.
You only observed the conversation that you observed. You did not observe all the potential conversations that might have occurred instead of the one you heard. The value of such conversations is the result of an expected value calculation, based on the potential benefit multiplied by the possibility that such benefit would be realized. That involves a lot of guesswork, obviously.
