Pete Buttigieg has leapt to the top tier of Democratic presidential candidates by touting himself as a moderate alternative to Elizabeth Warren and Bernie Sanders. But his economic platform still embraces an expanded role for government and a shift to the left.

Mr. Buttigieg has a Wall Street tax plan with new levies on financial transactions and capital gains. He wants to uproot decades of labor law, giving unions more clout to counter big business. And he proposes raising Social Security taxes and benefits, while also contemplating...