Man, I hate to get into these whizzin' contests, but, here it goes..
The S/D offers discounts to fill rooms that are not reserved, plain and simple.
Imagine going up against the Disney Marketing Machine, which is exactly what the S/D does. It's a tough thing to get people out of those Disney owned rooms into the S/D, so, there are multiple discounts offered as an incentive to make that happen.
Why those particular occupations?
The government discount, as stated, is offered at most chain hotels. Mr SwanDolphin(who used to be a frequent poster here)
just took it a step further and opened it to all government employees to get people out of the Disney owned hotels and into his.
Teacher discount--every year there is an awards ceremony at Disney for teachers. Why not entice them to stay at your hotel rather than another? Hence, the teacher discount. Since there was never anything that said it could only be offered during the time frame of the ceremony, it became available all year.
Nurse discount--this one is a little more personal. There is a Swan-Dolphin Cheerleader (the original ones--you can find them on the RB these days) who is a nurse. She kept badgering Mr SwanDolphin (and, after the birth of the Cheerleaders, they all became good friends with SwanDolphin) telling him nurses wanted to go to WDW too and stay at his hotel(,mostly just teasing him because of the teachers rate) His downfall came when he mentioned that his sister is also a nurse. The Cheerleader nurse then turned up the
pressure a notch.

Lo and behold, the nurse discount was born.
We have the discounts that we have because SwanDolphin is a nice man. There are discounts availabe for everyone at the SD and you don't have to jump through hoops to qualify, nor wait untill the last minute wondering if your dates will be included.
AAA, Entertainment book, AP. They are all easier to get than the Disney discounts and it's never "AAA who's been a member since 1954' stuff like Disney is pulling with their Visa Card.
Fair? Maybe not to all, but, then this world is not about fair.
But, there is a discounted rate for everyone out there. That's more than you can say about Disney.
OK--off my soapbox.