I think one of the most interesting things about homeschooling compared to trying to teach in a public classroom, is the easy ability to adjust based on a child's learning style. It's quite a monumental effort in a large classroom to even determine learning styles, much less meet each child's needs. While I don't actively homeschool my 3 year old, he is almost 4 now, and definitely wants to participate in school. Of course, his learning style and personality is almost a complete opposite of my oldest.
My oldest child is definitely one who does things because they are "supposed" to be done. He wants to see the boxes, check the boxes, and move on. While he did get a bit excited and work ahead in his math book, and he does usually finish up the read aloud books on his own, he also can be a bit hesitant to try "something new". He loves science experiments, but hates crafts. He also told me today that he "couldn't read" his history book on his own. I kindly pointed out that he finished the read aloud stories (approximately a 4th grade reading level) and had him read a chapter aloud, but didn't push him. Pushing him generally backfires, but I do require him to finish his work carefully.
My current youngest (for at least a few more hours, days, or weeks) is quite the opposite. Good luck telling him that he can't do something. I really have been trying actively not to teach him to read, but he keeps jumping ahead in leaps and bounds. We aren't actively doing phonics, but he has about 400 sight words at this point. Some of which are quite unusual and I wasn't sure where he was getting them. I finally figured out a few are from the video games that they watch on YouTube (many of the YouTube video creators narrate the written on-screen dialogue, so my 3 year old can now read "Port Prisma" and "Course clear" from Paper Mario Color Splash). He can usually read at least half or more words in a level 1 book. I suppose sometime after our 3rd boy is born, I will have to get into phonics so he's not missing out on some important reading habits. He is also more in tune with his fine motor skills so he loves stamps and do-a-dots and his favorite from his "math books" (which are preschool workbooks designed for 4-5 year olds) is to "cut and paste". I make him finish everything that comes before the cut and paste, but I don't require a certain number of pages a day. Sometimes he will ask to "do school" at random times of the day and do 5-10 pages at once.
In public school, kids can be labelled and put in groups and "advocated" for if they have special needs. In homeschool, they get to just be your kid. You can modify and adjust any curriculum to meet their specific needs, and even change curriculum entirely if something doesn't work for you kid. Since my oldest is a bit behind in fine motor skills still due to his sensory issues, we will be taking a break from our current curriculum when we finish out the current year, and try something a bit less writing intensive until he is able to catch up. It's a beautiful thing, and I can't wait to see what special personality and learning traits come out with the 3rd boy after he arrives and starts to grow and develop.