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.'