...why didn't science just do this in the damn first place?!
It's never been cost effective. The same way safe coal mining and 100% safe fly ash disposal isn't cost effective. If you need to expend more energy to deal with the waste than you get out of it, it's not worth it.
....but what does the "short-lived radioactive elements" dissolve into? surely not *nothing*? ...how much can we strip away through processes before every part is used? ...how little matter do we need left over before we can eject it from the Earth's atmosphere into the Sun?
If we get it to the point that it's economical to launch in a rocket, then there's so little left that storage shouldn't be a big deal. And if it's safe enough to put on top of a rocket, then it doesn't need to be removed from our biosphere.
Most of the really radioactive waste is extremely dense. So it gets insanely expensive to get it out of earth gravity well. To make matters worse, we have no space launch systems that are reliable enough to use for this type of disposal. It's one thing to have a bunch of highly radioactive material sitting around in a shielded location. It's an entirely bigger problem to have a failed launch blasting toxic crap all over hundreds or thousands of square miles/kilometers.
It's also a waste of of non-renewable material with a high amount of potential energy that we may be able to do something with sometime in the future as our understanding of physics progresses.
Even ignoring the huge amount of energy required to launch something into space, our current launch vehicles are not the most environmentally friendly mode of transportation either.