Self governance is a fundamental human right. However, all forms of government require compulsory membership, usually in the form of compulsory taxes. Without such compulsory taxation, government would seek to function because most people would choose to 'freeload' rather than pay their way.
Unions are very similar, in that they provide a valuable service to people. The difference is that the group is defined by employment within an industry, rather than geography. Unions also have a problem of freeloaders - people who benefit from increased salary and improved conditions, but who do not support the union financially. Many people see compulsory membership as the answer, however this clashes with another fundamental human right - freedom of association. In practice, many people just object to paying the high fees involved for a service they did not ask for.
This is where it gets a bit complicated, because many compulsory unions have mechanisms in place that keep fees high. While they may have originally been established to keep union income steady, they ended up becoming highly undemocratic tools. A classic example is compulsory student unionism at universities. The student body would regularly elect groups to power (such as the Young Liberals) who were ideologically opposed to the existence of the union. They would set about dismantling the union structure, to the extent they were able to. Despite all this, student union fees would remain remarkably high, given the low income of most members.
Perhaps an even greater barrier to democracy in these organisations is disinterest. It is hard enough getting people to pay enough attention to local, state and federal politics, without expecting them to get involved in the minutia of union politics. When people do get involved in their union, it is normally based around a specific issue, rather than union income.
A simple solution to all of these problems is to make each union election a referendum on union fees. This would provide sufficient motivation for people to turn up and vote. Even if they didn't know who the candidates were, they would have an opinion on whether the fees should go up or down. This could be combined with measures intended to stabilise union income, for example limiting the annual change in income to 10%, or by making the rate of change proportional to the demand for change - for example if 53.7% of members voted for an increase in fees and 46.3% for a decrease, the fees would go up by 3.7%.
This may appear to prevent the union from disappearing, because the members could never vote the union out of existence by lowering the fees rapidly. However, there would quickly come a time when the fees were no longer sufficient to keep the basic functions (such as elections) of the union running. Before that, the situation would reach a point where the union would actually get more income by making membership voluntary, but giving the executive more control over the fees.
So what is the government's role in all of this? Rather than supporting compulsory unionism or abolishing it, they should merely mandate that all unions with compulsory membership create a more direct and democratic way for members to adjust union fees.