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I'm not going to debate what the definitions should be, I'll just say I don't think it is productive to join an existing conversation using terms with different definitions than everyone else uses. Defining all housing as inherently "affordable" makes the term meaningless and even if you disagree with the motivations behind the desire for "affordable housing", at least the term has meaning in the way it's typically used.
You are quite literally debating what the definition should be, because this is _not_ the existing definition of affordable housing, it is legally what OP is saying. "Affordable housing" is just when the household spends <= 30% of gross income on housing related costs. This is the definition used by the HUD and the same definition applied in policymaking.

What >you< are referring to and what it is conflated with by progressive policymakers is "low income housing" which imposes an AMI based restriction on the resident's income. This in turn means that 30% of their income is much lower and restricts the sticker price of the home.

In recent years, most 'affordable housing' policy has been advanced by progressives, who use that term for marketing purposes, whereas the actual policy primarily relates to 'low income housing' or even 'very low income housing.' This does not mean 'affordable housing' = 'low income housing', it just means the term 'affordable housing' is used in the title and the actual measures advanced are related to AMI and 'low income housing.'

Those definitions aren't in conflict. The "progressive" definition is just the applied version of the "HUD" definition scaled to local income levels.
There is no "progressive" definition, income level is not at all part of the definition. Per the universal legal definition of 'affordable housing,' if a home costs $1B but is occupied by Elon Musk, it would still be affordable because it is less than 30% of his gross income.

When you are dealing with income levels it is universally called 'low income housing,' and the HUD definition is already scaled to local income levels, the 'A' in AMI stands for 'Area.'

You are conflating marketing ('we need more affordable housing!') with policy ('low income housing')

> There is no "progressive" definition

You seemed to disagree with that in your prior post, but I’m glad we can now agree that there is no point debating this then.

It is productive to decline to use propaganda terms. If, every time someone says they support affirmative action they are asked if they support having higher standards for Asian applicants to medical school than for white applicants that’s good because forcing people to defend their support of racist policies reduces support for them. By the same token pointing out that affordable housing doesn’t mean housing people can afford, it means politician allocated housing paid for by the general taxpayer, reduces support. Reducing support for bad things is good.
Its also helpful to know that there is a specific (US) program called "affordable housing" that subsidizes rents for low income people. The economic effect of that program is to increase rents (but not home prices). This especially hits the working poor who make just a bit too much to have subsidized rents.