It's easy?
a) it takes a team spot on your team, leaving more loopholes for your opponent to exploit
b) Spinners are easily predicted and taken advantage off
c) After the spinner dies, no guarantee your opponent can't take advantage and set up SR anyways
d) With the exception of Starmie(who has LOADS of weaknesses) and to some extent Tentacruel, most spinners are:
i) Frustratingly slow
ii) Little to no offensive pressure
iii) Easily dealt with
e) Rapid Spin gives the opponent a free set up turn(which can be catastrophic in some cases, like letting Landorus get a free Rock Polish).
I would certainly stop using spinners if weren't for Stealth Rock, even with Spikes. There are many Pokémon immune to Spikes anyway. Starmie is good but is outclassed offensively by Keldeo, with its only advantage being the extra Speed (however, Keldeo is stronger, LACKS a Pursuit weakness - in fact, it resists that move and threathens every single user of Pursuit - and Secret Sword is a better move to get past Blissey and Chansey than Psyshock). Tentacruel lacks any offensive presence, and is a rather meh Pokémon if rain is not active; Toxic Spikes are mediocre on this metagame. We all know how Forretress is setup bait for many top threats on the metagame, even those that it can potentially wall. It is also the easiest spinner to spinblock against (except against Gengar), lacks reliable recovery, and is outclassed as a wall by Skarmory. As for Donphan... Well, lack of relible recovery, no reason to use it over Hippowdon, and the fact that Ice Shard can't even 3HKO Landorus-T!!! says all.
I voted that I believe that Stealth Rock is not broken, but it would be interesting to see a metagame without it. Maybe it isn't better than a metagame with it? We do not know. Dragonite and Volcarona would certainly become the kings of metagame, but with Moltres being viable, other top threats like Sheer Force Landorus would become less viable (although I predict that people would then use more physical Landorus since it can lure and KO Moltres with Stone Edge). People are, however, forgetting that sun would also get a boost. Darmanitan would certainly love being free from the necessity to deal with Stealth Rock, and would have much more chances to spam Flare Blitz. Victini would love that even more, and since Victini is very bulky for an offensive Pokémon, it would have much more switch-in opportunities. Sun would certainly get an huge boost, and I predict that it would make a bigger impact on a metagame without Stealth Rock.
I also predict that both Sand and Heatran will be used more. Tyranitar can threaten both Volcarona and Dragonite with the right move as long as they do not boosted, and the sandstorm will become the easiest way to break Mulsticale. Choice Scarf Landorus will probably rise usage on sandstorm teams since it can consistently revenge kill both Dragonite and Volcarona. Heatran can also deal with both Dragonite and Volcarona if it runs an standard offensive set with Air Balloon (to avoid Earthquake and HP Ground), Hidden Power Ice, and Stone Edge (to OHKO Dragonite and Volcarona, respectively). Because sun teams would rise on usage, Heatran would also become much more useful. The only thing that would prevent it from becoming a staple on teams, would be rain.
Speaking of rain, Tornadus-I and Thundurus-T would be excellent choices, if not staples, for rain teams. Without having to waste a teamslot on a spinner, Gyarados would rise on usage because not only it can counter Volcarona that lack Hidden Power Rock, it also does not have to worry about Stealth Rock at all. Gyarados would also have less chances of ruining the defensive synergy of the team, since it doesn't force you to run Starmie or Tentacruel on the team (Forretress is a good spinner to run with Gyarados, but Starmie and Tentacruel are much better spinners on rain).
And Charizard would actually become a viable choice for sun teams. Lol.
On the Volcarona issue: it can opt to run Giga Drain to deal better with bulky Water-types and Ground-types and recover damage from Life Orb, while beating Terrakion and Keldeo, or it can opt to run Hidden Power Ground to defeat Tentacruel and Heatran while still beating Terrakion, or it can opt to run Hidden Power Rock to deal with Dragonite, Salamence, Moltres, opposing Volcarona, and Gyarados. Because of it and Dragonite, I think that people would use more revenge killers with Rock-type attacks to deal with them both.