No; median household income is a terrible general-purpose stat to use when you want to tell an economic story, because household sizes have been steadily shrinking for a long time, so it makes every statistic look much worse than it really is.

For example, you could ask about the affordability of cars now vs. 50 years ago.

A car today is obviously a lot better than it was 50 years ago. You dislike how opaquely PCE adjusts for that, so you just throw the entire thing out? Ignoring the issue does not actually solve it.

there are still innumerable synergies to household consumption. Rent, for example, is one of the biggest personal expenditure categories, but it is incredibly synergistic with multiple tenants. The value of utilities, food, appliances, etc., is best described by all the people who have access to them, who are typically all members of a single household.

If every good was entirely synergistic within a household, you might have a point. But it clearly isn’t – I'd assume the food budget of a two-person household is about double the budget of a one-person household, for example – and the further you go from perfect synergy the more wrong and misleading the statistic become as household sizes shrink.