That's great that it pisses you off and good for them that they have been given "a shot." However, this is a business first, and a sport second. If you don't get drafted, you instantly have a slimmer chance of making the roster than the players that were drafted. These "undrafted gems" you speak of don't show up very often and for every "undrafted gem" you can mention, I can mention a first round player that is considered to be one of the best in the game. The fact is most of these undrafted guys if any of them won't even see the third week of the preseason. No need to get offended, they are getting there chance and I'm sure they will make the most of it but don't expect them to go out there and make the team.
If you want to speak on "business", you should know a businessman leaves no stone unturned when looking to make a profit. Not saying they will make the team, but we had 3 of our UFA make it last year and helped this team in some way. It's possible it will happen again.
Also teams look for a chance to sign the cheaper guy to do the same job equally, if not better than the guy making more money that he's competing with. That would be the business aspect.