For many people housing isn't part of a basket, it
is the basket.
If food prices go up, it hurts psychologically but it's not the end of the world. I can buy cheaper food, I can buy less food, I can eat out less. Most people in the developed world are very far from food price-induced famine. I can buy a year's worth of sustenance for a thousand dollars, it might not be healthy but I'm not going to die.
Housing is qualitatively different. Many renters are only a few steps away from homelessness, and more people rent nowadays because they cannot afford to buy. It's hard to adjust for increases in housing costs by buying cheaper housing, your housing is linked to your income.
I complain about but don't ever worry about food prices, yet the roof over my head is a real cause for concern.
For my parents' generation it was the opposite, being overweight was more uncommon, housing was dirt cheap, people worried about getting enough calories rather than too many. Indexing wages to inflation is an anachronism that we have taken into this new world.