The US tax law and welfare programs are bastardized, redlined shitshows of laws that are frequently thrown together at the last minute and passed without anyone- even a staffer of a voting congressperson that read the whole thing. I don't know if the whole "equity disqualifies you from welfare" thing was explicitly added to keep people from owning houses and pulling themselves up by their bootstraps or if it is just the product of lazily written policy.
Lets be honest, what percentage of people getting benefits for being layabouts would actually be investing into a home if not for that rule? i agree the rule is dumb. Means testing as a way to narrow the benefactors of government aid to the lowest, least productive losers is what makes the democrat's policy strategy a) ineffective and b) alienating to a large portion of middle class people, who for example are ineligible for basically any of those campaign advertised tax rebates because they make $81k per year when the ceiling for income to qualify for any kind of federal tax credit it like $76k.
The other issue is that both parties campaign on big slogans like "welfare reform", which is judged by journalists, academics, and voters (lol not really) in dollars saved, or budget reduction. So, reforming welfare typically means reducing the yearly line item spend. How is this done? As lazily as possible with no consideration about the secondary effects, of course. Reduce the line item expense by narrowing the eligibility requirements. Easy way to do that is to just make it so anybody with equity in a house is not eligible. Boom, you just got rid of x number of people. never mind that because they no longer receive benefits they are much more likely to take out a second mortgage, default, lose the house and be back on bennies in a few years anyway. Who cares? by then, nobody will even remember who did what and when to the budget and welfare reform can be done again, making the system even worse.