In this thread i've read lots of theories about how broken rain is, but i have yet to see a log or some other sort of proof to support such a claim. B4 the Shaymin-S ban, i ran a team with a scarved Shaymin-S and no other water-type resistance or a weather setter, yet i never found it hard to counter drizzle teams. Now i use rain too and i have had only mediocre results with it. In practice, rain is much less threatening than what theory makes it out to be. There are countless ways to beat a drizzle team, even without a member specifically designed for that purpose, such as forcing Kingdra to lock itself in on Outrage or choiced attacks and revenging with a steel, KOing Kabutops with Mach punch, striking Manaphy with an attacker that outspeeds, while Ludicolo loses to any semi-bulky poke not weak to its STABs (Metagross, Latios, Breloom, Zuruzukin) due to its only average offensive capacity. Nattorei can also use any Kingdra as setup fodder to lay down spikes, which hurt toad every time it comes in to renew the rain, so clever switching among Ttar and Natt can stop such teams by itself (a common situation in my experience). Politoad's also a relatively bad pokemon for OU, unlike Ttar or Hippowdon. However, the main issue drizzle teams tend to face is how bad they operate outside their beneficial weather, unlike sun or sandstorm; a dead Politoad usually means GG, as any relatively fast and powerful pokemon (Latios, Gengar, Jolteon), will destroy a core of water-type sweepers. Paralysis also ruins the SS strategy, and some of its most common users just so happen to be nearly perfect to deal with drizzle teams, with Porygon2/Blissey shrugging off any attack Kingdra can throw and Voltlos/Erufuun crippling with priority, while the first has a STAB more often than not lethal for waters and the latter a resistance to surf/thunder. Storm drain Cradily uses any SS sweeper as setup fodder too. Trick Room is a pain as well.
In short, i find rain is overhyped. Unless somebody can provide proof to support the opposite, like a log of a low skilled player with a drizzle team easily defeating a skillful one with a non-weather or sand team, i believe in a metagame with so many competitively viable rain dance counters, drizzle teams are manageable. Trick Room Slowking/ Rankurusu/ Celebi, Sunny Day Chansey/ Blissey, Thunder Wave Gyarados/ Porygon2/ Voltlos/ Erufuun, Hail Kyurem, Water Absorb Suicune, Storm Drain Cradily, Nattorei, Calm Mind Kerudio/ Virizion, scarved Jolteon, Cloud Nine Lickilicky, are all examples of viable pokes which can severely cripple or even 6-0 most drizzle teams by themselves.
Regarding the argument "I must dedicate a teamslot to specifically counter rain teams": this doesn't mean that drizzle is broken. Dedicating a teamslot to counter a single pokemon is definately disturbing and constitutes to Uber status, however by using Nattorei or Virizion you become able to counter an entire playstyle; this is like claiming "stall is broken, because i must dedicate a teamslot to a wallbreaker". If a single pokemon (like Nattorei) or a single move (like Sunny Day on Chansey) allows you to essentially destroy an entire playstyle, then it might not be a bad idea to dedicate a team/moveslot to it.
Assessment: Drizzle is imo not broken. Gen 5 brought infinite rain in OU, but it also brought some near-perfect counters to accompany it. Banning Drizzle will not balance the metagame at all, it will just make sand the prominent weather and next suspect round people will start searching for other threats to ban.