If bringing your team together is the goal, it cannot be served by labeling those who choose to bring a lunch as "boring types". I know my feelings would be hurt if my coworkers decided to exclude me for that reason.

How does bringing lunch from home prevent team lunches? If it's scheduled ahead of time, it's easy to bring less. One might even be able to justify budgeting N lunches/month out with coworkers.

Also, lunches together don't always have to be in a restaurant. Buyers can get food to go, bringers can take theirs with them, and then you can either meet in a conference room, at a park, etc.