There is actually no difference between buffing the weak champions and nerfing the strong. They accomplish the same goal with the only difference being how easy it is to do such things. Even if you aimed to buff everything to be completely equal, it's inevitable that some champions would still emerge on top of all the others, which would then in turn require more buffs to everything else and the cycle would just continuously repeat.
For example, Lucian is currently very strong, but if you buffed Caitlyn just enough to be able to push him out of the bot lane then he'd be considered extremely weak, despite receiving no nerfs at all and would then need more buffs and the cycle would never end.
The only difference with nerfing things that are strong is that it's so much simpler and feels a lot more satisfying to see that champion you really hate seeing every game get put down a couple of notches.