Barriers to entry exist today, and will always exist in some form. The question is who gets to define them. I am arguing that the workers themselves should have more of a say than they do at present.
One union certification could literally be passing some randomly selected leetcode problems. Ideally, there would be a variety of certifications to reflect the variety of niches in software (someone doing TLA+ for embedded applications shouldn't need to know anything about web app architecture, necessarily).
The difference is that you wouldn't have to do it for every new employer, and workers would have more say in defining the body of knowledge considered relevant.
I don't think anyone would advocate for university credentials to be a hard requirement. I personally have no relevant university credentials except some math courses from a community college.
That said, I think it would be fine for someone to submit a transcript from a CS degree to be certified for basic algorithms knowledge in lieu of sitting an exam on that topic.
I'm an immigrant who finished a pure-math PhD and went into software engineering afterwards by building up a portfolio and leetcoding in my spare time. With your system there is no chance I could have done that. Passing all of the exams would not have been possible without a strictly CS education, and I couldn't have studied for the exams after my PhD finished because my visa status at the time was tied to being actively employed.
So many people nowadays are becoming productive software engineers from slightly unconventional backgrounds (pure math, physics, boot camps) and this would stop immediately if CS certification became part of the job requirements.