Actually you'd be surprised. Armor (to include tanks) has been shown to have a significant impact in many areas. Armor isn't necessarily destructive, and it brings in a presence factor that can intimidate (or make people feel more secure...including locals who seek government protection) without using its weapons. Should fire support or any sort of reaction force be required, armor is especially hard to replace. Many of the arguments you're mentioning were touted as reasons not to send armor to Vietnam.
To take one point: building rapport. The presence of armor can deter insurgent forces from moving into a village, and also can have the effect of making local populations feel more secure. Protection provided by armored elements can then allow more civic action elements to operate in the village, improving the quality of life in the area. And if the armor's held nearby, it can serve as a reaction force that's harder to stop than a leg or airmobile element.
Tanks don't always have to park on people's cars or vegetable patches.
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