i've been in effectively-invitational games that were low-profile minigames and they were good fun, but i doubt anyone got upset about not being in them because most people weren't any more aware of them than any other minigame.
so really it depends on what the purpose of the invitational is. if it's to be a focus of the site's attention as the marquee game of the year, then that's a bad thing, because exclusion from it is meaningful. if it's a way of putting together a bunch of players so as to create a unique play environment - one where all share a particular approach to the game, thus the invitational nature means that each player in the game will make the game that much more enjoyable for each
other
player in the game - then that's a good thing.any large invitational is probably likely to have elements of both the upside and downside.
i think in terms of small/low-profile invitationals, any non-first-come-first-served player recruitment basis needs to be monitored, but the principle is one that's sound and healthy in moderation.