The unique problem with the weather inducers is the fact that the weather stays on the field forever and forever, so, if I don't know, your inducer is K.O'ed (or if you don't have inducer), then your opponents will have forever, I don't know, rain or sandstorm for the rest of the game, you can't stall it, you can't change it at all, you can't remove it, you can't prevent it's effects at all (Rayquaza in ubers is decent, but Golduck...), so, that is the problem with the weather, it endures forever on the field, AND, you can only reverse it using other weather, and your opponent can just switch-in it's inducer again...
Also, it's overcentralizing the game with the inducers (a solution for this could be make Rain Dance move and stuff set longer, or eternal). But even the - eternal - rain and stuff could be ok as long a move who can remove weather and prevent it's modification would be created, like, Clear Sky, and the field could stay free from weather modification for, I don't know exactly, 5 turns (you're wasting already one turn, maybe 8 with an item).
Anyway, there are a huge number of Pokémon who were viable or were on higher tiers on the Generation III that losed it's OU or UU status JUST BECAUSE SR WEAKNESS, yeah, it's not only a thing of the x 4 weak, it's a thing of the x 2 weak, too, why? For the sweepers, it's hard to do 100% of damage to every Pokémon on the game, almost impossible, even with hazard standar hazard, you're still needing 88% or more to succesful sweep, but, what happens? Pokémon weaks to it are being punished, and sweepers ONLY needs to reach 75% of damage to OHKO it, and ONLY 50% of damage to OHKO the x 4 weakness, that's excesive game changing, that is excesive game breaking, and that's the main reason why the Tier List of the Gen III completely changed on the Gen IV (apart from the Dragon Zone because the buff to the dragons), while the Gen V generation did stay really similar to the IV one. If you're weak to SR, you need to be a huge, huge, huge powerful monster (like Kyurem-B, or Quiver Dance Volcarona), or you're just not viable, that's incredible.
You're trading the possible brokeness of just 2 Pokémon (I don't think Volcarona is broken without SR, Salamance maybe) by making more viable four complete types of Pokémon, some will became OU, and a good number UU, and RU, sun could not sucks (so hard) against rain, and a other good number of change to bring more variety if SR is just nerfed, but not removed or almost making it unviable. Also, there're a huge number of walls that are not utilized by just it's SR weakness, like the same Articuno (high UU on the past), who could stall for the eternity anything without rock attacks if not were by the omniprescence of SR crippling the 50% of it's HP EACH TEAM it switch-in's, amazing, and swepers are having it's time a lot easier, and cleaners, too (they need to focus less punch on those types), so, SR is one of the reasons that are becoming the current metagame more offensive-inclined, because you're already crippling any wall that is weak to SR.
