Indeed, Super Saiyan are extremely powerful, almost insanely so. Usually when one turns into a Super Saiyan, it's usually something epic. For goku, it was when Frieza killed Krillan, and it wasn't an instant transformation as well. For Vegeta, after days of non-stop training and almost pretty much killing himself, he simply stopped caring anymore. Something snapped inside him. For future Trunks, it was after seeing Gohan, his only surviving friend, die infront of him. The only exceptions to this were regular Trunks and Goten, and their transformations were a complete surprise to everyone (Hell, Chichi cried when he did).

In response to the idea that descendants of super saiyans can go also go super saiyan, I'd like to point to a main character of GT, Pan. Now, by your logic, since Pan's the daughter of a super saiyan, she should be able to as well. Well, throughout the entire series of GT, she never once went super saiyan. Heck, she didn't seem to be anywhere near as good a fighter as Goten and Trunks were at her age. This can be attributed to the fact that the saiyan blood in her is starting to thin, due to the fact since her father was a half-breed and her mother was human, she's pretty much a quarter breed. If this is going to be set in the future (which everyone seems to agree on), than all of Goku and Vegeta's descendants could have lost the ability to go super saiyan, and it's gone back to legend again.

I'm not saying we should ban super saiyans outright. I'm just saying that at the beginning, that power should be out of reach, but you should be able to as the RPG progresses. Don't feel that your character would be piss weak without it. Even without the ability to go super, Goku and Vegeta were still pretty powerful. Goku managed to hold his own against Frieza long before he went super saiyan.