This was a fascinating question to answer! One of the great adventures of American education is that the early 1900s, especially the decades between the World Wars, marked a whole bunch of negotiation around what kind of system was best for American and American children. Basically, it was a lot a philosophizing and pontificating by educators, mostly men, mostly white.

First, "Essentialism" was less about a way of learning and more about a way of doing education. It's important to keep in mind that three men who established the school of thought, William C. Bagley, Michael John Demiashkevich, and F. Alden Shaw couldn't agree on the best way to describe their philosophy, which is probably why you're having trouble getting your brain around exactly what it is. (Rest assured, so did I!) While Bagley's writing and Atlantic City speech appear to pushback against progressivism and traditionalism, he was challenging many of the same aspects of both that adherents of both philosophers disagreed with. In other words, he and John Dewey agreed on a whole bunch. Likewise, it's likely he and Charles William Eliot, chairperson of the NEA Committee of Ten and Carnegie Unit sherpa would have agreed on a whole bunch.

Second, the philosophy never really caught on in any meaningful way. I went through every ed history book I have in my collection and couldn't find a single mention of it. When it appears in ed philosophy texts, it's almost an aside except when one of the co-authors of the book has written extensively about Bagley. Even some of Bagley's most ardent biographers caution against drawing connections between the few texts focused on the philosophy in the 1930's and today. From Null's in-depth look at the origins of essentialism:

The study also demonstrates that any attempt to use Bagley’s ideas to support contemporary calls for “standards and accountability” rests on a weak understanding of the history and philosophy behind essentialism... Direct correlations between essentialism and the [modern era], however, are deeply problematic.^1

Which is to say, there isn't really an essentialist learning model to speak of; the roots of explicit, teacher-led instruction can be traced back to Socrates. Likewise, it's difficult to claim American students have experienced it in any meaningful way as it didn't find it's footing or make any real headway into the American education consciousness. So, it's difficult to compare "essentialism" to other theories as many of the writings about the philosophy are based on the author's interpretation of what Bagley may have meant. In effect, "Essentialism" is in the same memory hole as Froebelian and Pestalozzian education.

My sense is that, perhaps, someone was attempting to link current efforts around school accountability to historical movements. Essentialism, though, wasn't the starting point for tests and the use of their scores in a variety of ways. Tests have been a part of American education since the founding of Boston Latin in 1635 and Harvard in 1636. Admission into Harvard was partially or completely dependant on how well the young man who wanted to attend did on the admission test. This meant that parents, or the applicant, would often hire tutors based on the tutor's reputation on helping students do well in the admission interview. The tutor was expected to be an expert in a particular series of Greek and Latin texts that varied slightly from Colonial College to Colonial College (a previous question on the admission process.) Jumping ahead a century, there was a massive movement in New England in the 1860's to compare schools based on how well students did on written tests^1. (Before that point, schools would hold public performances, or recitations, to show how "smart" their students were.) New York State implement a statewide testing system, known as the Regents Exams, in the 1850's. By the 1930's, there were dozens of possible exam topic options for students and teachers. In addition, students in the 1700 and 1800s disliked homework as much as students in the 1900s and 2000s. By the time "essentialism" came along in 1930's, home work was very much a part of the American school experience. Granted, 13 years of school wouldn't truly become the norm until the 1960's, so the actual count of children who did homework at the time was relatively small.

A number of pieces I came across describe the philosophy as focusing on essential or critical knowledge all American students should have. This, though, is basically what's the "canon" is and despite progressivism's reputation, wasn't rejected by men like Dewey. Likewise, the liberal arts curriculum that has long been common in American schools came in two flavors: classical and modern. The classical liberal arts curriculum was based on a shared knowledge of Greek, Latin, some maths, sciences, and rhetoric. The modern curriculum, which slowly replaced the classical one over the course of the 19th and 20th centuries, expanded to include English, art, music, physical education, and multiple branches of math and science. As far as I can tell, essentialism had zero impact on the transition from the classical to modern curriculum.

So, now let's tackle the notion of "standardization" in your question. Two things to note. First, due to the 10th Amendment, education is a matter left up to the states. This is why, in 1939, as Dewey and Bagley were giving dueling speeches at a conference in Atlantic City, the legislature in Mississippi was finding loopholes in their compulsory education laws so cities legally justify denying Black children an education. While Bagley, Dewey, and all of the other men were themselves getting their college degrees in the early 1900s, various states and the federal government were placing Indigenous children in residential schools, often against their parents' wishes. In other words, standardization in American education is a slippery thing to pin down.

Finally, let's turn to teaching as a profession. While it's accurate to say the evolution of teacher training from a 12-year apprenticeship model (learn by watching) and a few years or weeks at a normal training schools into a four-year teacher prep programs granting BS in Education, teaching still carries the institutional memory of the feminization of the profession in the 1800's. In the 1600, 1700s, and the first part of the 1800, pedagogy (that is, the HOW of teaching) involved a lot of brute force. Boys, and sometimes their sisters, virtually all white, were regularly beaten for misbehaving or making a mistake. Being a schoolmaster was to be in a constant battle of wills with older boy students over who would dominate the classroom. Given education was primarily something for the sons of family with the means to pay a school bill or chip in to pay the teacher's salary, the model was sustainable as men would teach on their way to something else.

However, as the notion of a "common" school system for the sons (and sometimes daughters) of men of all classes spread across the Northeast, there was a clear need to expand the teaching force. As a result, there was a veritable PR campaign to rehab schools' reputation. Advocates worked to change the reputation of school as a dirty, dank place lead by a cruel master to a soft, welcoming space led by a kind, motherly young woman. He beat the children. She coddled and cared. (To be sure, this wasn't just an early shift to child-centric schooling - a la progressivism - but rather, in the eyes of the public school advocates, there were a whole bunch of unmarried white women sitting around not doing anything. Putting them to work as teachers seemed like a perfect way to meet a need.)

There was little or no pedagogical training to speak for most of the 1800's as the feminization of the profession was stepped in gender essentialism. That is, the prevailing belief was that women were born to be motherly and as such, would just know how to teach. This wasn't true everywhere, to be sure, but as a general rule, it wouldn't be until the modern era that the teaching professional established national credentialing and standards of performance. One of the key reasons this is important and how it relates to your question is that when one looks through documents related to "essentialism." Despite the feminization of the teaching work force (and the corresponding cut in salaries), men remained in education. At the classroom level, it remained a temporary thing men did in-between other gigs, often earning 3x as much as the woman teacher in the classroom before or after him. However, a new class of educators emerged: Schoolmen.

And this is the group our new friends Bagley, Demiashkevich, and Shaw belonged to. They were men (mostly white, non-disabled) who moved quickly in and out of the classroom, ascended to leadership positions - usually by recommendations from friends or former classmates - and proceeded to write books and papers on what they thought American education should be. As such, the American model of education exists in both theory in practice; one shaped by the men in positions of power, one shaped by the women doing to daily work of teaching.

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1 - Well, J. W. (2007). William C. Bagley and the Founding of Essentialism: An Untold Story in American Educational History. Teachers College Record Volume 109, Number 4, pp. 1013–1055

2 - Reese, W. J. (2013). Testing wars in the public schools. Harvard University Press.