The BLS agrees. That's why "shelter" is weighted 35.6% in the CPI basket, by far the biggest item.
> I couldn't care less about all the other categories, personally.
If we're going by what people "care" about (whatever that means), the basket would probably be like 70% gas prices, 20% grocery prices, and 10% for everything else. Empirically speaking, those two are far more salient politically than housing.