The problem is the fact that the Tiger is usually not alone, and there will be grens/shrecks & maybe a pak around. Swarming a Tiger generally means that your tanks need to be able to absorb some fire while they're in flank range.
I do like using the T-34 horde though, but the Sherman's cost and low HP make it not worth it in my experience. Just using tanks alone is a riskier way than making a general push with combined arms.
I much prefer if the Tiger attacks first, and then I hit it with a counterstroke (t-34s/shermans, infantry, Zis).
3 shermans easily kill a tiger. 2 T34/85s with mark target deal with it fine.
Manoeuvrable armour is my favoured way to tackle a tiger.