Let me start out this post by saying that I am in favor of the right of unions to organize, although I am not in favor of any special government protection of unions, including the prohibition of "yellow dog contracts". Unions can serve an important role in communicating information from low-tier workers to upper management. They may have lower transactions costs of coordinating certain kinds of worker activity than other forms of organization in some industries. If left to the competitive marketplace, we would only expect unions to survive in those areas where they are socially beneficial (again, absent any special protections).
Having said that, I would like to criticize a frequent justification for unions. It is often said that without unions, workers would be underpaid because they would have no bargaining power. If labor markets are competitive (that is, if there are several employers and several employees) then this is simply false. There is a reason why different people in different occupations earn different wages, and it has little to do with "power", and everything to do with Supply and Demand. IT workers are paid very well, until the supply of IT workers increases significantly, driving their wages down. Workers who work in oil extraction in the U.S. are paid one wage, but workers who work on oil platforms at sea for months at a time are paid a different, higher wage, because there are fewer workers willing to accept those conditions, driving supply down, and wages up.
In the absence of a labor union, workers in the automotive industry, writers in Hollywood, and truck drivers around the country would be paid the market wage. The market wage is the wage that sets the value to society of hiring one more worker equal to the cost to society of switching that worker away from doing something else. It is the efficient wage, and by that economists mean that it is the wage that maximizes the difference between benefits and costs to society. If the supply of workers is restricted somehow, driving the wage up, that does benefit those in the industry who keep their jobs, but it hurts those who are no longer employable at the higher wage. It also harms consumers of the product they are producing, because consumers must pay more in the form of higher prices and reduced output.
The writers in Hollywood are not facing a monopsony (a monopsony is a single buyer, whereas monopoly is a single seller). If they were facing a monopsony, they might indeed face exploitation as the single employer would pay less than the wage provided by a competitive market. But again, writers are not facing a monopsony. There are many companies hiring writers, not only in Hollywood, but around the country. Writers also have alternative employers, such as magazine publishers (when they write magazine articles) and the consumers themselves (when they write books). The fact that not everyone who wants to make a living being a writer can do so is not a market failure. Rather, it is an indication that some people should not be writers. The ultimate protection for workers is the choice of different employers. If no employers are willing to hire a worker for a wage the worker will accept for a job the worker wants, then the worker should consider a different line of work. Furthermore, an employer which consistently underpays its employees relative to its competitors will find that its competitors are quite willing to hire away the best workers. Employers do not pay the market wage because they like workers; they pay the market wage because the market leaves them little choice. If you don't believe this, then consider yourself in the role of buyer: When you walk into a store, can you dictate any price for goods you buy, regardless of market conditions? Of course not; the seller of goods will not sell to you if you are not willing to pay enough to justify his production. You cannot exploit the seller of goods if there are other buyers of goods, and the seller cannot exploit you if he faces competitors. The same argument applies to buying and selling labor as surely as it applies to goods and services.
The "power" paradigm of wages is bankrupt. It has no explanatory power. Do finance professors get paid more than economics professors because they have more "power"? Of course not. The reason is that finance professors are more useful outside of academia than economics professors; the demand for their services is greater. Schools must pay them more to lure them to the academy, and away from other opportunities. This is Supply and Demand. If you want to equate "greater demand" with "power", then I suppose you could do so, but I think that is an abuse of language. To say that the result of the uncoordinated, decentralized decisions of thousands of employees and employers is some kind of power struggle is bizarre.
Perhaps you feel that, even at a market wage, writers are underpaid. If so, rather than arguing in favor of a non-competitive labor market, won't you consider arguing in favor of income redistribution instead? If your concern is that workers are too poor, income transfers are probably a less costly way to achieve your goal than a labor cartel.
I've seen it argued that labor unions are simply the result of the free association of individuals, and should not be prohibited. I agree, but I wonder if those who put forward this argument would be willing to apply their logic consistently--say, in the case of product cartels. A group of business leaders who voluntarily agree to impose higher prices on consumers are doing the same thing as a group of workers who voluntarily agree to impose higher wages on employers (and again, the end result will likely be higher prices for consumers). As it happens, cartels usually fall apart because it is hard for each firm to stick to the agreement, and the same might be true of some unions, absent government policies to protect them. Collusion is collusion. If you're going to stand up for collusion in the name of free association, at least be consistent about it.
One last point: It is frequently argued that labor unions were once necessary, but they are no longer necessary. If you look at the data on wage growth in the U.S., you see quite clearly that wages grew quite rapidly before unions rose to power, and this wage growth continued after they came to power. There may have been a few circumstances of monopsony in which workers were taken advantage of, and in which unions were genuinely socially productive. I think that in general, however, the social contributions of unions throughout history have been oversold. That is, labor unions may never have been necessary, at least in most circumstances. We should not make the mistake of believing that just because something did happen, it is what should have happened.