Well that is a post factum economic explanation. They were established to protect them from unhealthy/ unworthy working environments. Nowadays they do raise the price of services artificially, but not arbitrarily by any means. If the standard of living goes up but paychecks don't, that's when syndicates act.
Actually, no. They were established (or at least finalised) during the late 1800s. At the time the vast majority of those who worked in factories (of their own accord) came from rural areas where their families owned land. At any point, the majority of workers could've moved back to their homes. They chose not to because the working conditions (and pay) were better in the factories than on the farms. The imagine of the factories the most have today come from the use of de facto slaves. These de facto slaves were orphans under the care of the government which were leased/loaned to businessmen who were part (or in bed with) the British oligarchy at the time. The only way for salaries to go up is if there competition between employers for employee contracts. Standard of living (by which I assume you mean the price of consumer goods and services) usually goes up because of cartel practices enforced or inadvertently created by the government. Usually because of monetary inflation caused by the government printing money but also because the government's doing things governments usually do like waging wars or impeding trade.