Just need to set the record straight here. SSJ3 does NOT require full Saiyan blood. Reasoning for this is because Gotenks went SSJ3.
A common argument against this point is that when Goten and Trunks fuse they become a full blooded Saiyan, but they forget that being half Saiyan also makes you half human. 50% human, 50% Saiyan. Goten and Trunks are both half Saiyan, so when they fuse they are still only half Saiyan.
I suppose you could argue now that SSJ3 requires half Saiyan blood, but I honestly don't think that's the case either. I think it has more to do with potential power than anything else. You could only half a drop of it and still achieve it IF you have the potential. We don't have the potential to even get Super Saiyan 1 by ourselves.
As for SSJ1, in all honesty I've always viewed Super Saiyan in DBO as more of a Pseudo-Super Saiyan. This explains why it doesn't give a very large power boost. We just don't have the capacity for anything more.
Anyone who would say we can just wish for SSJ2 and 3, that's not going to work either. Shenron is not all powerful, his abilities are dictated by the limits of his creator. Just giving us this Pseudo-Super Saiyan form and Dragon King's buffs, I think he's pretty much tapped out.