As I am a great fan of experimentation, I'm generally in favor of Blizzard trying this out. It's content that is completely new, that no one is invested in yet. So it's a perfect ground for trying something new.
However, let's analyze things further. First, let us separate idea from implementation.
The central idea of the Brawler's Guild invitation is to have a content gate that depends on other players. This is very different from most content gates in WoW. Most content gates are independent of other players. Whether or not your character is attuned to an instance really doesn't depend on anyone else. It solely depends on your own efforts and those of your guild.
A content gate that depends on other players has been tried once before: the opening of the Gates of Ahn'Qiraj. That too was an interesting experiment, and is remembered by Vanilla players. It was memorable, but maybe not entirely successful.
However, unlike AQ, this gate is not all or nothing. Rather, it is set up to spread virally throughout the population, a la Gmail. Perhaps this will prevent large population spikes or activity that hurts the servers. Maybe this will have positive benefits, or maybe artificially preventing some people from the content will be negative.
Either way, I think the idea behind the invitations is interesting, and worth experimenting with.
Now, the specific implementation of the Brawlers Guild Invitations is to sell them on the Black Market Auction House. Many people instinctively rebel at giving the "rich" people initial access to content. However, there are some advantages to this method.
First, everyone who buys an Invitation wants an invitation. They are deliberately purchasing the item, not picking it up by accident. That means that there are no "wasted" invitations, and the number of invitations is strictly known.
Second, this method allows a consortium of people to band together and purchase a set of Invitations.
Third, this method is not random. It is guaranteed, while still limiting the number of available Invitations.
Fourth, this method does not disrupt the rest of the economy or the playstyles of people not interested in the Brawlers Guild. Imagine if daily quest mobs had a chance to drop the invitations. People farming the mobs for invitations would conflict with people who just want to do their dailies. As well, there would be a large influx of farmed materials like cloth, which would temporarily depress prices in the regular markets.
Now, there are other ways Invitations could have been handed out. You could hand out invitations to people who could kill a heroic raid boss. Or maybe the PvP's who win the most arena matches each week. But this too is just as elitist as giving it to the rich people. And these people already get first crack at new content.
It could be purely random, but that would just encourage people to farm futilely, or have some invitations be wasted.
You could put the item on powerful rare spawns. But then there would be intense camping of those rares. And how would you deal with raid groups that killed the spawn? Look at the competition for things like Loque when it first came out, and imagine it a thousands times worse because killing the spawn actually unlocks new content for all classes.
To my mind, selling the Invitations on the BMAH might not be the best possible idea, but it might be the one with the least side-effects, and thus, the least-worst idea. All the other ideas I can think of are either too baroque, or will negatively impact people who are not interested in the Brawler's Guild.
Plus, you know, this method hasn't been tried before. Killing bosses and the like has been done before. I think it's worth experimenting on something relatively low key like the Brawlers Guild.