Domestic help was once available because there was an extreme surplus of dirt poor people.
After the economic boom due to rising productivity, there weren't enough dirt poor people willing to work for peanuts, and today things like minimum wage and various benefits programs make it easier to not work for so little money a middle class family can easily afford it.
People would rather buy cheap factory goods than the more expensive hand made ones because they prefer to spend money on other things instead.
Google says the average barber haircut in 1900 for a man (women often did their hair at home) was 25 cents, which is just shy of $10 adjusted for inflation. Most places around me offer basic haircuts for $20.
In 1900, only the state of Minnesota had a requirement for barbers to be licensed (it was the first state to do so, in 1897). No beautician school requirement, no licensure payments, no state or federal income or sales taxes.
In short, it's surprising that the rise in cost of a haircut hasn't been higher.
I think there's something to Baulmol's theory, but there's a lot of hand waving that isn't really supported as well by the examples given here or elsewhere that I've seen. That, or the effect isn't all that it is claimed to be; it's almost tautological that as supply of workers for a low paying job dries up, the wages for the job have to go up to retain workers.