If there is any general trend at all, it would have to be that the younger the non-established board, the less likely it is to be closed off from the Internet world at large. Less established boards, like less established "real" life neighbourhoods, tend to encourage new traffic, new members, indirectly new povs, indeed often try to obtain them by any or all means possible: since it is precisely upon such traffic that a new board lives or dies. Established boards (however young), on the other hand, have a definable base of "regulars" who can be relied upon to keep the board alive and active of themselves, regardless of outside interest and participation.
The more reliable the "regular" traffic, the less necessity for a board to require outside participation for its survival -- and the more the group identity of those who frequent the board becomes uniquely defined.
Around this point, "require" gradually becomes replaced with "permit".
Not all outside participation is generally found desirable: spam (unsolicited and repeated advertising) being the usually cited example. However, as core identity gradually gels, the specific type of outside participation tends to become less distinct (spam, member of a linked board, curious passerby seeking a home), blurring eventually into one vast category of "not us, not invited, 'Do we know you?'".
Perhaps such increased polarisation between "us" and "them" is inevitable. Those participating actively or passively from outside the regular group are rather less likely to invest in the group identity to the extent of core members. Thus, in their passive or active participation, any outside potential can present a threat to that same group identity regardless of actual intent. At one extreme, even the possibility of lurking defines the potential of some viewpoint, somewhere out there, which may not conform -- and which, in addition to its possible active disruption of the evolving group identity at some future point, also tends to undermine the group identity by its sheer existence.
The solution is to close off specific, protected parts of a board ... and finally the heart of the board itself, first simply from general posting, then even from viewing. The more a board closes itself off, the less likely it is to obtain any new traffic whatsoever except by invitation: perhaps the ultimate in isolated elitism -- but also the less likely it is that someone whose views might not conform to the whole might stumble across the board at all. It can be argued that the closing off is not two-way -- those within the closed community still have the option to wander outside -- but, with increasing degree of insularity (and thus "safety" in a "refuge"), such outside wandering among those whose viewpoints do not to some extent conform (or, often, are found "worthy") becomes increasingly unattractive compared with the "safe" alternative.
A parallel argument can also be made that without some degree of non-invited outside participation, a board must eventually stagnate within its own increasingly insular identity, given that it only ever can have the reinforced views of its own members upon which to build. (The distinction is made because only such participation as is already known to conform to the board identity will ever be "invited".)
There is an interesting "real" life equivalent, also undertaken willingly and voluntarily, to such gradual shutting away of all outside opinion and eventually all outside contact -- but does the parallel apply in the Internet world?
Are restrictions on the poster any less powerful for their having been imposed voluntarily by the poster themself?