Safeguarding could be solved via video calls with health visitors. Which would actually be safer than a nation of latch key kids.
Latch key home educated children already exist, if by latch key kids we're meaning those at home without their parents. That's already a thing, been well known to happen for years. Home educated children are meant to have access to the school nurses team (not health visitors, they're largely too old for that), but how well that works depends on your area (I say as someone who is still waiting for my 16-year-old to get the jabs he was meant to get at 14).
I'm a home educating parent and have been for over a decade. I chose this option for primary for all of my children. I do not want the government to pay me for this choice. As has been raised on home educating sites when this comes up, if the government gives money, then the government can rightfully expect certain results. In areas of the US where money is available to home schooling parents, it's generally limited to certain suppliers and it is not uncommon to expect evidence of education through yearly exams or having a portfolio checked by a professional. The UK doesn't really have that market of home education focused creators to be able to create an acceptable list of suppliers, teachers in the UK have enough to do without being pushed to check the work on home educated children and British home educators largely don't want the government involved in what we do. Low income home educators are already eligible for benefits as much as any other parent.
If we're talking about improving the system, I personally would be happy if the government just covered the cost of exam fees for home educated teenagers who are compulsory education age and provided guaranteed exam sites. School educated children could also take extra exams if they desired.
If we're talking superwish list, funding to ensure the school nurses teams could be accessed by all home educated children who wanted to talk to them and that the computer systems that people use to register their choices for places at primary and secondary could include a home education option so we didn't have to deal with places being allocated to us that we don't want, that'd be great. Maybe even, when there are events where school children can submit work publically, home educated children being included in that more so they can feel more part of the community even if their local school isn't an appropriate fit for them.
Really, there are a lot of things I can think of that could help home educated children that would make it more of an option that parents could happily choose rather than now where it's mainly a choice because everything else has failed, but none of it really involves paying parents the money that would go to school. It's more funding for things that would include all children in the community regardless of how they're education.