EC education has two goals.

1. Babysitting. But "high quality" baby sitting so that higher SES parents don't feel guilty about prioritizing income and career over offspring.

2. Babysitting. Whatever that means so that lower SES parents don't have to worry about their offspring and can say that their kids' education isn't their fault.

3. Closing the achievement gap.
A. Behavior: Exposing children to enough structure, enough interactions that are appropriate for kinder, so that behaviorally they act like the children of those who were middle and upper-middle class 30 years ago. It's "socialization" but to some extent acculturation. Whites were acculturated to this decades ago, and now, sadly, a lot of people with a 18-second time horizon tend to view this as acculturation to "white values." They weren't "white values" in 1890. Much of this is play, but not parallel and more structured. (For high SES kids, whose parents overstructure everything, it looks like unstructured play. This says a lot about the writer.)
B. "Academics": Exposing the kids to a rich enough vocabulary and syntactic structures that their lexicon and grammar are at what is considered developmentally appropriate for the start of kinder. This helps their phonology: If you aren't exposed to enough tokens of sufficient words, you don't develop phonemic awareness, and without that you're at a disadvantage with reading. (And, no, phonemic awareness cannot be taught; it is emergent, as anybody familiar with the phonological literature for the last 10-15 years would know. Education faculty tend to not like this because it makes them less savior figures and more facilitators, but most of the phonological discussion in educational literature was obsolete in 1990.)
C. Life hacks: Knowing how to button clothes, tie shoes (if appropriate), knowing basic colors and such. Yes, this is vocabulary in part, but tied closely in with realia and skills.
D. Context. Being familia withr and having done many "enrichment" activities that are part and parcel of growing up in a middle class, fully staffed household. Knowing how to handle having a book read to you and treat things, do simple kinds of experiments and tasks.

Most kids are still full of awe in 2nd grade, whatever their backgrounds. Instilling it into them in EC is rather like teaching them how to breathe in kinder.

Notice that high quality EC for middle and upper middle class is a political and "me too" sort of thing, with politicians pandering to such voters in exchange for support. Their kids don't suffer from it, but don't benefit from it. A lot of people support the idea of universal EC to avoid the stigma of just having those kids who need it get it because all they see is race; low SES whites benefit just as much as low SES blacks, but that's not how helping just low SES families is perceived by anybody. Note that I entered first grade unable to count to 5 or knowing basic color terms. I knew no letters of the alphabet.

Government supports it because government's chief role is supporting the role of government. Sort of along the lines of "The bureaucracy is expanding to accommodate the needs of the expanding bureaucracy."