Here's more of my opinion on the subject. Feel free to skip it.
According to the Declaration of Independence, rights are not granted by government. The rights to live in liberty and to use one's liberty to pursue happiness are endowments of the Creator. Because they are unalienable, even the disrespect and trampling of those rights by tyrants does not take them away.
Shelter is not an endowment of the Creator; human beings in their natural state are not endowed with access to shelter; it is not unalienable. The natural law governing shelter is work: human effort must be expended in order to find or create it. A lack of effort is all that is needed to alienate us from shelter. The need is a natural incentive for the effort and having the need satisfied is the natural reward for expending the effort. Therefore, shelter is a human need, not a human right. Because we all have a right to liberty, no one has the right to tyrannize another by taking shelter they create or find and using it as their own without the consent of the person who expended their own effort to create or find it.
When government attempts to endow its citizens with a new right-a right to something that requires human effort to create or find (as opposed to unalienable rights that are endowments of the Creator)-it can only do so by taking that something away from someone who has expended effort to create it, find it or otherwise make it available, either by direct force or by forcibly taking money and goods away from the citizens in general to compensate those who create the object to which it is fabricating a right. If the government attempts to endow its citizens with a right to adequate food, for example, the government must take food away from those who produce it or take money away from the citizens in general to compensate the producers. Artificial, government-endowed "rights" come at the price of enslavement of the producers or enslavement of everyone.
Whenever a citizen has a need met without expending effort (especially through government intervention and redistribution), the incentive to expend the effort is reduced or removed altogether, less and less effort is expended to meet the need and shortages result. This has been proven in every utopian society ever constructed, including the former Soviet system. Not only were architects and citizens in general enslaved under the Soviets, but the lack of housing became worse and worse until the system was overturned. A "right" to shelter did not make shelter appear; it created less and less adequate shelter. No policy or incentive within that system was capable of correcting the fundamental flaw: disincentives.
I agree that a major contributor to homelessness is the disparity between housing prices and the ability to pay of those at the lowest levels of income. However, unless the government forces someone to provide housing against their will or takes resources from the citizens in general to incentivize housing production, the natural incentive to create it is left to the market. An oversupply of housing has the general tendency of depressing prices, which is good for those with low incomes, but it also removes the incentive to provide housing except by those that are producing for altruistic reasons, rather than as a way of earning a living. Once housing production slows down as a result, the supply lags behind the demand and prices rise, restoring the natural incentive to create it. The dampening force of this pendulum is altruism. I believe most architects are naturally altruistic, but few are willing to live in poverty themselves in order to provide adequate housing for others. And the altruism of architects alone does not result in housing-only designs for housing. A great deal more altruism is required to make it a physical reality that actually gives shelter.
I conclude from this that the best way to combat homelessness is to use our altruistic motivations to combat poverty and mental illnesses in the private sector, helping more individuals become able to pay the market rate for their own shelter while motivating the natural housing market to produce as much as possible. That is how we can make the world a better place. The true moral issue is liberty and the true design problem is in creating and using altruism-problems that are not at all unique to architects.