Because a wet-bulb temperature of 35C is generally considered deadly, perhaps as low as 31C. Global warming that kills large swathes of Burma or India would be a household term I'd think.
But "heat index" is already a household term, and essentially has the same purpose [0]. It's like saying the Kelvin scale will end up in household use: I would disagree because while Kelvin is useful, it's not sufficiently more useful than C/F for most household usage.
> people cannot carry out normal outdoor activities past a wet-bulb temperature of 32 °C (90 °F), equivalent to a heat index of 55 °C (130 °F) [0]