I call bullshit on that. Source is a singular quoted number in a "National Alliance to end homelessness" report, which is not a government resource. Aside from small sample effects, there is just no way that a homelessness statistic of 'only 500k' on a single January night as a maxim is accurate. It also ignores the use of prison as a way to have a shelter, which is something homeless people tend to prefer over freezing to death.
And with mentioning that, that might also explain the lower number: they only count people specifically entering a shelter, who aren't using a variant of it somewhere else, like family and friends. As such, this number isn't even remotely a suitable to determine or get a handle on the concept of homelessness.
The European way of tracking tends to be by person and their registered address, with the shelter data just being a subset to compare with. It's comparing apples and oranges, on a time scale that says nothing.
But nice try to fly-by discredit otherwise proven sensible policies in other countries.
(greatest country in the world, right?)
btw, the report goes on to mention 7 million Americans were 'shacked up' with relatives, and the primary reason the shelter number is that low is due to the unexpectedly low unemployment numbers of the US. As is fairly common knowledge at this point: people don't need to be homeless when they have jobs, even if it's by paying rent to relatives.
But that also means that any change in that employment number for the worse will quickly change the homeless number.
additionally, the two targets you cherry picked to discredit these points are the only two other Western countries on the planet to get weird about very select ones, like a steady minimum wage, which the UK doesn't have. Canada is similar to that.
Everybody else in the 'west', in this case confined to Europe, is within the 0.2% number and is likely tracked in a more reliable manner over a longer time to boot.