As I mentioned, it could ,and probably should, be both invitation and non-invitation. And just because a man is invited, as Bloke alluded, doesn't mean they are a shoe-in. Again, that'd allow for better filtering and vetting. I think allowing non-invitees is perfectly fine for sure. You wouldn't want to miss out on great candidates but this formula with no solicitation has led to the version we have now in the U.S. where our only goal is to keep lodges open when in reality, some of them simply may need to close due to 'lack of business'. I would rather them close than to allow just anyone into the fraternity. If these men could invite fellas they may not be closing after all plus they would be guys they know and trust.
In Turkey, men are invited and I'm sure other countries as well that is the case. It's close to impossible to get in if you are not invited. That may be overkill but inviting allows more control for the members to bring in fellows they personally know. Nowadays, a guy shows up with a petition, he meets once with someone at the lodge and a few weeks later they report and then vote....95%+ of the time he gets a yay and we allow some clown in that shows up in blue jean shorts and a AC/DC t-shirt on his initiation night. That's literally happened and not at all uncommon. I've seen a guy turn in a FC cat lecture in baggy cargo pants and a t-shirt. However, if that's the culture of your lodge, then that may be perfectly acceptable.