What hn_throwaway_99 means is: If the policy was "Homeless people rent a house of their choice and the state pays the rent" or "homeless people get cash to spend as they see fit" it wouldn't matter if there were low minimum standards and shitty houses on the market, as they would be rejected by everyone looking for housing - including homeless people.

In contrast if the policy is "Government pays the rent on the cheapest houses on the market, for homeless people" or "government has a fixed budget and must house as many homeless people as possible" then the legal minimum standard is crucial, because that's what you'll likely be giving to homeless people.

For councils to build houses and build them to a reasonable standard would, as you say, be another option.