The Republic had done little over the past sixty years but facilitate three major civil wars and sweeping domestic turmoil. The Senate as an institution had been a tool of the extremely wealthy old families, and many of their branches were by then extinct, either due to the Second Triumvirate's proscription lists or because many prominent Senators had sided with Antony in the final civil war. The Senate that was left was not really a worthy partner in government, and competition for the highest office would just lead to subsequent waves of civil wars on behalf of competing oligarchs.

You mention Augustus' family upbringing as populist, and the Caesarian tradition was indeed populist. Caesar himself got ahead in part by playing the masses' adoration of him against the Optimates, and to do that he had to be actually beloved by them. Augustus had no reason to believe in the Republic vs ruling as a strongman through popular support.

Also note that Augustus kept the forms of the Republic alive. Want to run for consul and have the year named after you? Knock yourself out. Want to seek a proconsular appointment as governor somewhere afterwards? You have the list of Senate provinces. Want your own coinage? The bronze coins can still say SPQR, the silver and gold ones will have Augustus' face on them. These nobles can now run the hamster wheel of the cursus honorum to their satisfaction without having the danger of holding actual power.