This is the salient point here. It's not the not getting tickets that people are getting emotional about, it's getting close to them and the system saying no (profile, payment, criteria). If that's sorted, and people just missed out on the luck of the draw, then it would be accepted. This is unfortunately where Ticketmaster falls down, it is a system aimed at placing 30,000 people in an arena...obviously the "criteria" are not met more frequently when you open up a 1,000 venue to 5,000 people, all buying tickets individually (thus taking up dots on the grid) or for up to four (?) people in their network. This is where an urgent rethink is necessary.
On the "fairness" issue, if a massive stadium tour of Your Favourite Band was announced, then there are usually ways to be more sure of getting a ticket. Buy the latest album, be on a mailing list, or whatever to get a pre-sale code. What you can't then do is say "right, there are far more requests than tickets available, everyone prove why they are worthy". To say nothing of the resources that would take even if you were mad enough to do it. So you can't introduce a points system at this stage, as mentioned above...everyone who bought a season ticket and parted with a wodge of cash at the start of the season should all have an equal chance of getting tickets for a game like this. 5000 into 1350 doesn't go, obviously, so there will be people disappointed.