No, that is not my entire argument. (However, ASIDE: when every advanced nation disagrees with your view on morality or pragmatism, it does not mean you a wrong, but it does mean you should closely examine your line of reasoning for both pragmatism and consistency with reasonable and well-grounded moral standards. Of course the democratic consensus of all of these countries can be wrong, but it's worth taking pause. That's all. END ASIDE.)
Here is the argument that I have been expressing in various forms and you don't seem to understand or provide cogent counter-points to:
PRAGMATIC CLAIM: Employers are allowed to "discriminate"/select based upon non-intrinsic signals of characteristics relevant to the job at hand.
WARRANT: This is necessary for society/businesses to function because otherwise, it would be prohibitively expensive to hire people using anything other than coin-flips.
MORAL STANDARD I: In order to use a signal as the basis for a hiring decision it should be both a) non-intrinsic, and b) signal something relevant to the task at hand.
EDUCATION MEETS THIS MORAL STANDARD:
a) CLAIM: Education is non-intrinsic
WARRANT: It is something you seek out and work to earn, not something you are born with. (The issue of ensuring universal access is entirely separable (and something I support, btw).)
b) CLAIM: Education signals something relevant to the task at hand
WARRANT 1: Technical background is assured through testing in relevant coursework -- testing that you would have to (at great and impractical expense to the business) reproduce in order to make informed hiring decisions.
WARRANT 2: Education can also serve as a signal of necessary problem solving ability, communication skills, etc.
MORAL STANDARD II: Any moral constraints placed on the set of available signals should not make it prohibitively expensive for business to function.
EDUCATION MEETS MORAL STANDARD II: Because it's a cheap signal to use as an initial filter.
BANNING THE USE OF EDUCATION WOULD FAIL TO MEET MORAL STANDARD II: It would require companies to essentially require a comprehensive examination that is well-proctored etc, which is a pretty huge burden for the company and -- besides -- basically would amount to credentialing anyways because any reasonable firm would outsource this.
Other relevant claims:
CONSISTENCY CLAIM: There exist signals that meet both standards.
WARRANT: Education can be used to select a small number of applicants, and the cost for choosing among those should be marginal wrt the value-added by the employee.
CLAIM: These moral standards preclude the use of race/sex/age discrimination.
WARRANT: these are all intrinsic features that are explicitly forbidden