I'm not unschooley at all, and so my answer is quite different from the people who think that 6 year old homeschooling doesn't have to look educational (I am more Montessori-minded, and early academics is something that happens in Montessori). I'm also of the opinion that in general, most children, if not given an appropriately prepared environment that lends to progression in academics, will naturally flock to activities which are recreational in nature. Even as adults, we'd rather play than work. So, even child directed learning must involve a carefully prepared environment given by adults in my own personal opinion (which obviously not everyone will agree with). So, I'll come at it from that perspective...
First, keep in mind that you said that the school days are too long for him. So, of course when he gets home all he wants to do is play. He's spent the entire day at school working! I wouldn't blame him...as an adult, if I worked 8 hours a day, the last thing I'd want to do is come home and do more work.
Second, he's 6. Six year olds are really still very young children, and don't really have the capability to understand the consequences of big life altering decisions like "do you want to quit school and stay home". They're going to agree with the thing that seems the most fun now. Case in point--my 6 year old, at the end of May last year, said he hated school with a passion. He wanted to homeschool. He begged every day to homeschool. I asked him why...he said he hated the teacher's rules. (Aaaah, he forgot that I have more rules than his teacher. :lol: ). Fast forward a few months to October. I asked him what he thought of homeschooling now, and he said that he loves school and doesn't want to be homeschooled. He has a lot of friends this year and enjoys the school's curriculum. So, in the span of a couple months, he changed his mind, solely based on what was happening in his life at that moment in time.
If you do decide to homeschool, you can take his learning style into consideration. If he's a visual and hands on learner, for example, having a math & science curriculum based on manipulatives (Montessori, Math-u-See, etc.) can work really well for him. And keep in mind that even the most strict classical education isn't going to take 8 hours a day every day because you're working one on one with the child, instead of 1 on 30. So, even if you give him a carefully prepared environment, it won't take up an entire day. (And what I mean by carefully prepared environment is that I will look at what the content standards are for the particular grade level in all areas of curriculum, and make sure that each homeschooling day, there are things across all domains that work towards those goals. I may alter the "exterior" so that the child is interested, and the child will decide to choose that work, but I know that everything in that room meets academic content standards. For example, if I want the child to learn addition, spelling words, handwriting, and sequencing that week, but the child is really really into animals, I will use toy animals for counting/addition, have him spell words that have to do with animals, habitats, and animal care, write about his favorite animal, and sequence stories that have to do with animals.) It can take a lot of work, so if school is working for your child except "he hates worksheets" and there are no real problems, then I'd think very carefully about whether you really want to put the time, money, and effort into it. If you do, and it is the right choice for everyone involved, then it can work beautifully (when the child doesn't want to, or the parent can't/won't put in the time/money/effort, I've seen homeschooling work really really badly. But when the child wants to and the parents are really invested in it, I've seen homeschooling work absolutely brilliantly!)