How was big business regarded by the harding, coolidge, and hoover administrations? as something that had a responsibility to all the people as the basis for tax revenue as america's most important strength as something to be regulated?

As america's most important strength.

Explanation:

In the 1920s the wealthiest Americans (top 5%) earned around one third of the nation's income.

Back then, the working middle class was not the largest social class in the nation, most Americans should have been considered poor, while a small but very powerful and influential upper class existed. No politician would have dared to even suggest limiting the influence and power of the rich people (the owners of big businesses).