Not sure your scenario is really about being friends. Choosing to take care of a child is more about my situation, than how much I might like them. If you are only taking care of a child because you like them, you are putting them at a lot of risk. Even great kids will be challenging, and a decent person cares for them even when they are unlikable or downright awful. That's pretty much the definition of unconditional love (though, reading through the comments here it sounds like a lot of lemmings didn't get that growing up).
As for, would I like myself? 10 year old me, sure! We share a lot of interests (I'd love to dm a game of dnd for him), and although a kid can be quite annoying, I think I'd be pretty fond of the little fella. I suspect I'd also gain a lot sympathy for my parents, and would love to try supporting him with some of his creative projects that he was always starting and never finishing.
20 year old me? Probably too wild to be close friends and I'd think he was an arrogant idiot at times, but probably find him kinda hot so I'd let it slide (my 'type' is pretty much younger me...). 30 year old me? Not all that different, could definitely be friends!