I do not think I could disagree with with much more than I currently do.
No, what was proven by Coolidge is you let the market bottom out, like it always had in what they used to call "panics" and then it starts rebuilding itself. Problem was we had, also under Wilson, established the Federal Reserve that had too loose a monetary policy which led to easy money, i.e. buying on margin, sometimes as little as 10% down, and then speculating in the market leading to higher stock prices, resulting in a frenzy as more was borrowed and invested leading to overproduction... blah blah blah, and then the Fed tightened the money supply when they should have been there for the banks, supposed to be the lenders of last resort, banks started failing by the thousands... A president does not control/regulate the Fed, only appoints the governors with Senate approval.
Had we never involved ourselves in WW1 there probably would have never have had to be a WW2. The Germans made their last push, exhausted themselves and the front was more or less stabilized, as it had been for years... they fought to a standstill and all sides, exhausted would have been ready to sue for peace like they always had before. But with the US coming in on the side of the Allies it became a crushing defeat for the Central Powers upon which the Allies, especially Britain and France, put the boot on the neck of Germany, emasculated them taking away their military, assessing grand war reparations, blaming the Central Powers for everything. They redrew lines, carved up the Ottoman Empire, etc... what a mess that didn't have to happen if we had not come in and made equal sides lopsided in favor of the Allies.
WW2 went smoothly? What, all that world wide destruction and over 60 million lives lost? Surely you jest.
Booming economy? We were in massive debt and a recession after WW1... he helped create the recovery by letting the marketplace do what, if left unfettered, the American marketplace does best.
FDR get us out of the Depression? WW2, the unnecessary war,is what got us off the wrong path to nowhere FDR and his "brain trust" had created with all the government intervention the executive, his party and the Congresses of the time promoted. What was shown by WW2 was that all the while we were in Depression, from '29 under interventionist Hoover until hit at Pearl Harbor in '41, was that we had the capacity to produce one hell of a lot more than the policies of Hoover and FDR allowed, and we had a workforce second to no other that beat, productivity wise, our enemies combined.