I understand the impulse to identify some period in the past as a "golden age" for liberty, but it's dangerously misleading. Such arguments are going to always be horribly repulsive to non-white males and anyone who appreciates the history of their oppression.
The 1920s did see woman's suffrage, but it was a nadir of American race relations. The idea that it was a golden age for women and blacks is an absurdity- this is the height of the Klan revival we're talking about, the peak of angry mob lynchings in the South, and women got the vote but not much more. And the tone-deaf pining for the past is going to alienate all those many Americans- including most white males- who rightfully regard now as the free-est time in American history. For every one complaint you have against the Feds today, and they are many and weighty and deserve to prevail, I could provide many more serious and violent attacks on human liberty in whatever decade past you wish to select- the 1770s, the 1890s, the 1920s, the 1950s, etc.
Also the "no welfare state" thing, in addition to being not entirely true, plays directly into the hands of the narrative of pre-progressive America as a robber-baron-enslaved hellscape.
There's a lot to be good said about Coolidge, no doubt about it. Rescuing his reputation is a great idea. But the liberty movement shoots itself in the foot with a retrograde attitude of"why can't we just got back to [insert mythical golden age here]?" Few things could appear more abhorrent to the uninitiated.