Eating together can be accomplished through culture alone but providing food is probably easier and more successful.
I have worked at a lot of different companies, and an ad-hoc, employee-organized lunch run is very common. The person who commits to handling the cash and picking up the food decides on the restaurant, orders are placed by a deadline, and people eat it when it arrives. If a manager or admin staffer names the restaurant, they have to say whether the cost of the meal is on the company or not.
Occasionally, someone will name a sit-down restaurant and a time of day, and people simply show up.
People who don't want to participate on any given day don't participate. They eat the lunch they packed from home, or go somewhere else.
That's how grown-ups eat lunch. If this pattern does not arise naturally, there is some dysfunction in the workplace that should probably be solved directly, rather than trying to force the pattern into existence by providing catered lunches.
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.
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.
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.
Now people just sit at their desk and check Facebook/reddit/etc over lunch — or they break into cliques. As a junior employee, I found that free lunch leveled the playing field. Senior managers couldn't hide out with only other senior managers when you all eat at the same place.
They say that the family that eats together stays together and I think that's just as true for work families.