As most of you know, I am both a homeschooler and a public school educator.
As a homeschooler in a relatively low-regulation state, I've appreciated the freedom to submit a minimum of paperwork annually--especially in contrast to the extremely paperwork-intense public school environment in which I work. But I also recognize that my children are in the segment of the school-age population who would likely have had generally good outcomes regardless of schooling format (not that there would not have been different costs to different forms, but that most of the long-term costs would probably have been in my personal distribution of time and effort devoted to creating collaborative solutions with those settings).
We also live in a community that has provided a very high level of access to public school services for homeschoolers, including many of the items (other than funding, of course!) proposed by Kai. The district offers a couple of informational and support meetings a year, and will provide resources for curriculum, networking with other homeschoolers, and access to public school courses (short of all core subjects) and extracurriculars, including sports. I haven't interacted with this aspect of my district of residence, but I do know that districts in which I've been employed have provided special education services to homeschoolers, including OG reading, speech and language, and OT.
The annual progress report can include a combination of standardized testing and portfolio/work samples. The adminstrative designee actually reads both the proposals and the progress reports. (The first year we submitted a proposal, I received a prompt email respectfully requesting further information about reading instruction. My reply included documentation of reading mastery, to which they offered a cordial response, and clarified with more student-appropriate ways of documenting reading development.) Not surprisingly, I do tend to overdocument, but have learned to pare down to the information most valuable to them.
IOW, I'm in the population of homeschoolers that would find additional documentation and monitoring requirements redundant, and possibly experience them a little bit as overreach. But then, my children are not in the at-risk population that is the concern of the persons in the originally-referenced symposia.
As a public school educator, my experience with homeschooled children includes the concerns about at-risk and abused/neglected children, but with some additional nuance. First, there are absolutely families that use nominal homeschooling as a cover for abuse/neglect--but many of the ones I've seen who do so continue to interact with the public school system. (Granted, selection bias has to be in play here, since obviously, the ones who never interact with the public schools would be very unlikely to pass through my professional orbit.) The effectiveness of the public schools to screen for that particular kind of at-risk child is often limited by transience; these parents may pull their children out of schools as soon as questions start being asked--and then enroll them elsewhere, not necessarily to "homeschooling". These are also the same families that don't submit annual physicals and immunizations to public schools even when they are enrolled there. In short, the families we aren't seeing now would likely remain invisible even with greater homeschooling documentation and supervisory requirements, and the ones who would be highlighted often are already visible to the system. This doesn't mean there is no value in discussing thoughtful changes in oversight, of course, just that one should be aware that, like many other regulatory and legislative reactions, there would be a risk that it would adversely affect many law-abiding citizens, and only a few perpetrators.
On the much less severe score of inadequate education, I would agree that the average homeschooler is much more effective at teaching reading and writing than at mathematics and science. I should note, though, that this is also true of the public school system. (Leaving out history/social studies, as this is not assessed in most high-stakes testing, and can't easily be compared across populations anyway, due to differences in state content requirements.)
Compulsory education laws don't begin until at least age 7 in 15 states (with two at age 8), and end at age 16 in 14 states. Believe me, enrollment in public school by no means prevents parents from legally signing their children out prior to high school completion.
So I'm not really trying to make any particular point here about specific actions, just to reflect that abuse/neglect among homeschooling families is only one of the many manifestations of abuse/neglect of children, and, while some regulatory response to it is likely reasonable, it would be wise to include that as only one component of a broader and more thoughtfully-conceived rethinking of our entire societal approach to the prevention of abuse and neglect. Reactionary, expose-driven legislation is likely to disproportionately affect the innocent, without necessarily having the desired effect on the guilty--who, in reality, are often less monstrous (though their actions may be), and more misguided, ill, or in need themselves.