@OP: it doesn't matter if the "I don't want you in my group because your spec sucks" is a problem or not.
The main "issue" with specs is that it would require probably between a year or two of work, scrapping completly the current system.

Obviously, they won't do that.

The only way they could to it in a reasonable time frame would be to add a bunch of useless and uninspired passives to give the illusion of choice... and I don't think that's what you or anyone want.
So, I'm sorry but your post is completly useless since it's not doable without investing a lot of time and money while changing the habits of a lot of players (and possibly lose them as a result).

Anyway, if you just want to debate if yes or no a bad spec would make the player unable to be taken in parties or not, go ahead. But just keep in mind that it's all moot since they won't re-redo their game again for that.
If you abolutly love specs, just go find another game at this point, because they'll never come to FFXIV.