We haven't really decided what we're going to do with our kids. I personally think I'd enjoy homeschooling them, but I don't know what their preferences will be. Their mom would appreciate the break. That said,
1. Teachers develop skills in managing rooms of ~30 kids. I believe this is completely different from tutoring someone 1:1 and likely has very little overlap.
2. Part of my day job is already mentoring/teaching. I enjoy that part of my work. I've received feedback that I'm good at it. Actually when I was younger I thought I'd switch into teaching after building up some savings with programming. I've since heard/read enough about the realities of being a teacher that I can't imagine doing that job (especially with public school). Homeschooling or teaching a homeschool pod seems like the best way to actually be able to teach if that's your inclination.
3. The k-12 curriculum is not really much to cover. Schools move at a pace appropriate for the slower kids in the room. It doesn't seem like a high bar to beat, and most of what I've found looking into it indicates that homeschool parents generally do outperform schools with a fraction of the time spent.
3a. I've already been teaching my 3 year old phonics and reading when she's in the mood. She doesn't really have the attention to sit and focus for more than ~5 minutes, but that's okay, and it's still going alright. I expect she'll already be years ahead of the school curriculum before it's even time to start. So initial results have been promising and suggest I am indeed capable of teaching a child.
4. When it comes to more advanced/in-depth understanding, I don't expect teachers to have the background. Like just looking at the math education program at my alma mater, there's no requirement for real analysis or algebra. There's no requirement for science courses (physics, chemistry, etc.). All of the options in the math department except education require at least a minor in another STEM subject. It's no surprise that a common trope is that teachers (particularly math) don't know how to answer how something gets used in the real world, but that's insane to me as a status quo. There are tons of applications of pretty much any math you might learn before graduate level in pretty much any field you examine (conic sections stand out to me as a niche thing that we covered in high school. Not that they don't have applications to e.g. orbits, but they don't seem to apply to other fields, and I don't believe the connection to physics was made in my high school class anyway (presumably because math teachers where I grew up aren't required to learn physics)).
Honestly I think school is mostly more useful for socializing and something like arts/crafts that entail mess and require a bunch of energy to do at home, especially before high school/AP classes. The academic part seems trivial. Once you've reached that conclusion, it makes sense to ask whether there are alternatives that are better suited/are more aware of and aligned to their purpose as enrichment.