That is really not possible in accounting, which is something completely different from bookkeeping. Lawyers go to law school and doctors go to medical school for a reason.
An accounting degree is preparation for entry into a profession. Trust me, there is lots of “on the job training” required after the degree.
It takes years of on the job training to be a competent CPA or attorney. I’m both a lawyer and CPA and can say with certainty there are no shortcuts. And for the record, the bar exam was a breeze compared to the CPA exam.
When I graduated all of the Big 8 firms had strict requirements for new hires. I started my career with Arthur Andersen in a tax consulting role. I can’t imagine what that job would have been like without an education.
Accountants, lawyers, and doctors have very specific licensing requirements.
That doesn’t mean that the only possible way to gain the knowledge is higher education, just that higher education is the only way to gain the necessary licenses.
Self-teaching and apprenticeships can be used to gain just about any knowledge or skill. That knowledge could be used to pass certification tests like the bar exams. That society could choose not to recognize that knowledge or proficiency because of the way it was gained is a separate issue and says nothing about the competency of the individual.