Under right to work laws, unions still exist. Employees are still welcome to join unions.
That is true. But, because duty of fair representation, a union is supposed to represent every worker in a group, even if they aren't in the union. This creates a few problems. Nonmembers of a union can force a union to represent them, and this happens often. It just makes it harder for the unions to help the workers if more people are taking advantage of the union while not paying dues.
RTW has also been argued by some people (like
this guy) as a violation of the freedom of contract and association.
Workers in right to work states also make less money, receive fewer benefits, and are at a higher risk of workplace death than workers in non-RTW states.
Only three states in Lincoln have RTW laws anyway, and Michigan's exempts certain unions from its law.
In fact, right to work laws keep unions from becoming corrupt (going back to my example), because people aren't forced to join them.
Unions can become corrupt even if people aren't required to join, and corruption in unions isn't really that common. (Unions are generally more transparent and leaders are more easily charged for wrongdoing than in business or government.)
Just to make fhtagn happy, I might make a bill which details what unions and employers can and can't do. (It would just be a copy and paste of the bullets in
this link.)