Most folks outside economics see licensing as a way of legally certifying duties and providing a means of redress when incompetence occurs. Not only does a plumber who consistently allows sewer gases to enter a home get sanctioned civilly, he can be sanctioned by license loss and prevented from harming other households.
Let's try two examples on our theoretical plumber here:
1) Say that we have a local economy in which licensing is not mandatory. If I want some plumbing done, I have several options: I could open up the phone book, call around, and hire the absolute cheapest guy who says he's willing to give plumbing a job. He may do a terrible job, and set sewage to run through my ice maker. And I'd have little redress because I can't have him de-licensed. Alternatively, knowing those dangers, I could select someone who belongs to a plumbers guild or voluntary licensing organization which certifies its members as having a minimum level of skill and kicks out members who have complaints against them. This guy would cost more, but I'd have reasonable assurance that he would do quality work. A third option would be that I could talk to friends who've had plumbing work, or check through my KofC council in order to find someone who, while not certified, I'm willing to trust is going to do a good job. I check his references, and decide to trust him. In all probability, his rates are going to be somewhere between the person with the expensive license/membership and the guy who has the absolute lowest rates. The tension between these different groups will keep prices at a fair equilibrium. If the plumbers' guild starts getting greedy and raises their rates too high, then more people will do the work to check referrals and find a good non-guild plumber. If the guild makes it easier for people to be certified, more plumbers will join (in order to get more business) and this increased supply will drive down the price of guild-certified plumbers, etc.
2) Now let's imagine a situation in which the local economy is restricted with mandatory licensing. You can be fined or otherwise sanctioned if you work on pipes for pay without being a licensed plumber. On the bright side, this would suggest there's a certain minimum quality level for all plumbers. If you hire some guy in the phone book and he routes hot water through your toilets, you can call the licensing bureau and file a complaint -- given enough complaints, he may lose his license, thus protecting other consumers. However, there's now a mutually beneficial relationship created between licensed plumbers and the licensing organization. If existing plumbers can get the licensing requirements made more difficult and onerous, then they have less competition and thus have more secure work and higher pay. If the licensing organization can get away with making the process more expensive and onerous, they get to make more money. Say that originally you had to take four classes followed by a practicum test to become a licensed plumber. If the licensing organization raises its prices for the classes, or raises the number of required classes from four to six, they make more money. Better yet, the best and largest plumbing certifying organizations can turn to the government and try to get all their smaller and cheaper competition de-certified, so that everyone will have to go through the best possible (and most expensive) training. The only people with an interest in not artificially restricting the supply of plumbers are consumers, but it's hard for them to have any voice in the situation.
Now, if there was a way to keep the licensing process no more onerous than it had to be, I don't see that it would provide a huge amount of drain on the system. However, this brings me to what I think is another one of the basic differences in thinking between progressives and conservatives when it comes to economics (BA points out, rightly I think, that progressives tend to discount limitations of supply while conservatives tend to discount limitations of demand): One of the most identifying tendencies of the progressive worldview seems to be the assumption that it is possible to create institutions which are primarily ordered toward the common good -- not toward the good of the people who control them. Thus, it seems fairly progressive to assume that mandatory licensing will be used primarily to protect consumers, and that no one will co opt it in order to make the licensed profession more lucrative at the expense of consumers. Conservatives, on the other hand, tend to assume that regulations and power structures will naturally protect themselves while preying on others, and so they tend to see licensing as a way of keeping people from entering a profession while charging customers higher prices.