Home schooling takes extra work to add socializing, public schooling takes extra work to add one on one instruction. Generally. There are exceptions out there, and there are opportunities to hybridize the practices. But again - that takes work.
Public school also functions as a means to take the work of watching and educating a child during the day off of parents’ plates, so they can remain at least partially employed, or even just have a small slice of their life back.
Homeschooling is a luxury most can’t afford.
During the five years I homeschooled my daughter, I found that this was true but with one enormous caveat. We’re a secular family and homeschooling in many areas of the U.S. means that these groups are often organized around non-secular activities and principles. To each, their own. But I’m not going to sign a “statement of faith” to participate in a homeschool group. As a consequence, it really did feel that we were going it alone. Larger metropolitan areas are probably more inclusive; but otherwise secular homeschoolers have struggles in finding the right fit.
Many people select places to live based on school districts; it may make sense to put the same amount of weight on quality of homeschooling options. But even then, that's not going to be universally available in a nearby location.
There are also potentially online groups to connect with others (even more so now than when I was that age), which could help with finding and organizing groups.
It doesn't need to. Many areas, particularly those good for homeschooling, have tons of social and extracurricular activities available specifically for homeschoolers (such as by being intentionally scheduled in the middle what would otherwise be school hours).
And, of course, those are just the mass social activities, as opposed to small groups of friends.