We are talking 1v1/solo BGs here, not arena. In arenas warriors work just fine, due to the fact you got a healer holding your hand. They are more than viable for arena, but they will have a tougher time the higher they go.
You're actually dead wrong here. It is casters that scale the most with gear in TBC.
The reason is that while warriors stamina/strength stats, along with weapon damage goes up, the opponents armor, resilience and health values increases much more and so effectively nullifies the extra damage. Meanwhile warriors health pools are already high and so you face a diminishing returns in terms of gains for each extra health. Not to mention the resilience for warriors on S2, S3 and S4 gear is the same, while for other classes it increases.
The biggest changer though will be spell haste. As it in 2.4.3 reduces the GCD most casters will have 1,1-1,3 second GCD (depends on gear setup) while warriors, retridins and shamans (enh) and hunters will be stuck with a 1,5 sec GCD. However the hunter class will not be that touched by this. Rogues also suffer from this issue, but not as much because of their stuns, non GCD Shadowstep, vanish, evasion etc.
This will drive warriors mad as they realise that for example a druid can Root/Cyclone them within their 1,5 sec GCD span - without being able to do anything about it, as all your abilities share GCD and so pummel/shield bash is effectively locked out. Leaving only intercept as an option.
Oh and rogues will never have any problems with warriors. The insane amount of dodge combined with crippling poison kiting will make the warrior wanna go /AFK and read the news.