Such logic fails on a number of levels. First, there are unlimited number of potential jobs in a free market, otherwise everybody since Adam would have been unemployed. Given that there are millions more jobs available now than there were 100 years ago illustrates the point.
Secondly, it is healthy that some jobs disappear. The wagon wheel manufacturers and blacksmiths are not missed, nor are the scythe-wielding farmers. In terms of comfort, life was considerably harder back then, and more precarious. A doctor was as likely to make you better as he was to inflict additional injury via misguided treatments.
Some jobs evolved, while others disappeared and millions of new jobs like those involving information technology and the modern service industry appeared. Flight attendants and computer programmers were unimaginable 100 years ago. Any attempts to artificially keep wagon manufacturers in business beyond their usefullness would have led to enormous resource misallocations.
By allowing wagon manufacturers to slowly disappear as cars displaced horse and buggy, a sudden mass layoff was avoided and wagon manufacturers could gradually be integrated into other occupations as they became redundant.
As machines reduce the burden of repetative tasks, and populations become more educated and skilled, life gets better. Hong Kong and Singapore were the havens of low-paying, ¨sweatshop¨ labor only fifty years ago, but their populations have risen to become among the wealthiest and best-educated in the world as their skills and technology improved. At the same time that they have become wealthier, we in the West have not become poorer, nor has the total number of jobs in the West fallen. The common belief that low-skilled manufacturing in China and elsewhere will reduce quality of life world-wide has no foundation in history.
The number of available jobs and potential wages are limited only by restrictions on the elimination of redundant jobs and legal barriers to entry for new competitors or enterprises. Regulations restricting layoffs, working hours and days of operation, like Sunday opening restrictions, can only reduce employment. The true cause of unemployment and reductions in living standards is the lack of free market competition.