To be fair, as a fan of Final Fantasy, should it bother you that they are trying to get old / less interested players back into FFXIV: ARR?

Nope. It sure as hell shouldn't.

Does it bother me? Sure. I'd love an invite, but it doesn't ruin my day or compel me to complain on the internet about how it went down. I'd rather they send the invites to try to convince people who are on the fence, not those of us who will play it regardless. Hell, I'll sub to ARR for years simply because I believe in SE and I appreciate the amount of entertainment they have provided me over the course of my life.

The best way I feel they could deal with it (Not that they even have to) is just have rotational selections. I don't want to play the alpha for long. 3~6 hours straight would be fine for me to get a complete sense of where the game is going, how it plays, and what I should expect. I'd then gladly let someone else give it a go.

Alas, that's just not how it's being done, and you have to accept that.