By artificially limiting the number of invites, you get a finite number of individuals to work with and get feedback from during your beta.
I'm not sure the referrals program is always the solution you want. You should try to make sure the people who are coming to your site are qualified, otherwise Joe will ask Alice, Bob, and Charlie to join. Those 3 won't stay for any meaningful amount of time (blowing 3 of your slots), and Joe now has upgrades/perks/???. It's more desirable for you to have those 3 users giving you input.
However, there could be a time when you don't want to limit invites, such as when you need user generated content. Then the more beta users you have, the more content you have generated when you go "live".