If someone thinks the Government doesn't solve problems, they can just look at the 1929-1934 and how problems got "solved" under free market capitalism (before the massive government interventions starting in 1934).
(we now consider that period to be a giant mistake specifically because the government did not do enough and left free markets to their own accord)
No "we" do not, some people do, some people do not
There is LOTS of scholarly economics works that shows government intervention in the markets not only lets to the crash, completely extended the length the crash.
Specifically the fed actions in 1929 lead to prolonged pain not seen in other nations that recovered faster because their central bank did not try to "solvable the problem"
To state that is a forgone conclusion that everyone agrees that "free market capitalism" was the cause of the great depression is highly ignorant
(we now consider that period to be a giant mistake specifically because the government did not do enough and left free markets to their own accord)