I was often told I should use a corporation structure instead to save on taxes. The corporation would pay me a small salary, large dividends, and make zero profit, so zero corporate tax. Saves on self-employment tax, too.

That was incomplete advice. That would be correct if you were a C-corp, but if you are an S-corp or an LLC filing as an S-corp, you pay yourself a salary that is supposed to be within a plausible range of what you would make in your line of work, so you pay FICA and regular income tax on that. But there's no federal income tax at all on an S-corp. So everything left over is paid as dividends and it all falls to your personal income tax return, avoiding FICA and higher personal income tax rates. The logic is that the owner avoids double taxation of being taxed on corporate profits, and then being taxed again on the dividends.

Avoiding double taxation is fair in my view, but where it starts to get wonky is if you own say, eight used car dealerships, pay yourself $100K a year as a manager, and then book $1 million in dividends.