I believe the union-busting tactics of the 20th century are a big reason for the corruption of many unions: the ones that could stand up best to union busting were the ones management and politicians were physically afraid of meaningfully challenging.
That said, I live in North Carolina, where public sector unions are illegal (no state, county, or local agency is allowed to engage in collective bargaining with its employees). Sure, there are things like the NCAE, but in practice they're all completely powerless - aside from creating proposals which the NCGOP will subsequently ignore in favor of diverting more public funds to under-performing for-profit charter schools under the guise of "school choice," the only thing the NCAE really provides to teachers are benefits that the state doesn't. To quote a comment I wrote last January (https://news.ycombinator.com/item?id=29885392):
> There's also another factor at play: in many states, the power of unions is quite weak. E.g. public-sector employees in NC cannot collectively bargain, which is why they're able to get away with paying teachers horrendous wages. Want to strike? Go on ahead, pay your sub for the day (or your contract will not be renewed) and go down to Raleigh, where the legislature will recess and most of them will literally just go home and ignore all the people with picket signs.