Yes, most aware citizens know that today's voting processes are generally clean. There are still violations in every election, of course, and people still go to jail for it. That shows that the voting integrity processes work. The biggest recent scandal, involving 35,000 votes in North Carolina registered by a contracted Republican operative, resulted in a do-over election and jail terms; the system works.
There are states that deliver the vote without outright corruption. For instance, New Mexico has a powerful Democratic machine that delivers the vote based on social pressure, food give-aways (hams and turkeys at Christmas, classic), and "normal" local politics. That was the secret behind the former ward boss/union boss system in the Rust Belt states.
Regarding Huey P. Long, my understanding of his power base is the same as yours, that he didn't have to resort to tail-end ballot box stuffing as did LBJ. Long already had everybody in his pocket. There was considerable buying of individual votes throughout southern Louisiana in particular, though. Five dollars and a shot of whiskey was the going rate for black votes in southern Louisiana, ten dollars for white votes. Those voters actually voted legally in their own names, no identity fraud. Regarding Leander Perez in Plaquemines Parish, it was said that FDR only feared one man: Huey P. Long; and Long only feared one man: Leander Perez.
Bonus trivia: Louisiana is still ranked as the
most corrupt state in the Union, based on Federal corruption convictions. It's far outpaced by the District of Columbia, though, the most corrupt by quite a bit. The most corrupt city, by the same measure? Chicago.
Measured by the force and scope of anti-corruption laws, California has the toughest regulations, followed by Washington. By that measure, North Dakota is the easiest state to buy a politician - no limits on direct contributions by anybody - followed by Wyoming, with very few regulations against buying a politician.
