When Stones were introduced, barring Eeveelutions, it was supposed to be a punitive measure for people who evolved their Pokemon too early. As in "congratulations you've got a Pokemon with better stats and presumably more battling use, but since you evolved it instantaneously here's your handicap." It also rewards Trainers who, for example, persisted with their weak as fuck Vulpix till level 40 or so till it had Flamethrower or what not. And throughout the generations they've stuck to that pretty consistently.
Trade evolutions are different, if the same applied to them nobody would use a trade evo because after all the hassle you want something that's an improvement all around on what you had. You could say that people who use stone evos want the same thing, but stones are easily obtainable in-game (friends and alternate systems are generally harder). Also as in the Scizor one you mentioned, some Pokemon get new types and it wouldn't make sense to not have them learn new moves to match. (In Scizor's case, it learns Steel-type moves where Scyther had Bug/Flying/Normal moves).