This is why I much prefer Chinese (and similar) rules with area scoring. In area scoring you get one point for each space you surround, and one point for each stone on the board. It's immediately obvious and simple.

In Japanese rules you lose points for playing in your own territory. The black stone in your example is dead, and a reasonable player would allow it to be removed, but there's nothing stopping them from claiming it to be alive and forcing white to play to capture it. At this point the only option is for white to dispute its life status, and to duplicate the game board and make a hypothetical sequence of plays to prove it to be dead without actually playing the moves. There's a lot of added complexity for no real benefit, because the end result is usually identical.

I still prefer Japanese counting since it takes a lot less time to count (at least for me) a full 19x19 board. The only way white loses points (relative to black) by being forced to "play it out" is if black passes -- but the AGA resolves that by requiring you to give up a pass stone as a prisoner when you pass, and if the game has ended and you have to play it out, passes aren't allowed.

The next AI challenge is to have the AI make an argument that will convince everyone to adopt the One True Most Elegant Ruleset for Go. (http://warp.povusers.org/go/RulesElegance/ is an interesting page, along with his proposal: http://warp.povusers.org/go/MyRulesProposal/)

Chinese counting is just as fast once you're used to it. Remember that you only need to count one player under Chinese rules. And the AGA rules are a nice hack to Japanese rules to make them always give the same result as Chinese rules and avoid trolling/unreasonable plays, but it's still more complicated to explain to beginners than Chinese rules.

Yes, I always teach novices with area scoring, because all of the "if I played it out, I'd kill you, but I don't have to actually play it out" stuff is incredibly confusing to someone learning the rules for the first time. It's much nicer to have no penalty (other than opportunity cost) for playing these sequences out.

The AGA system of pass stones, bringing area and territory scoring into alignment, is very nice, but I think it's still a bit abstract for someone who's just starting out.

But in practice there usually ends up being no difference in score under either ruleset, or by at most 1 point difference.

A computer will correctly score that b as a dead stone, since it can't possibly make life, and white can kill it. That insurmountable threat makes the territory white's.

If a human tries to argue that b is alive, then either (a) that human is a novice, you can teach them, or (b) that human is a poor sport, and you shouldn't play with them.

Japanese counting is like Chinese counting, but assumes your opponent is not a jerk without explicitly handling cases when that's not true.

If a group is dead, it will be automatically captured at the end of the game.

So, in this case, the black stone is auto-captured, and you get the territory within as well.

So, yes, playing white stones to capture is actually detrimental to yourself. But also imagine if black keeps playing. They would be giving away free captures since black can never create eyes. And once the space is almost filled white can play 1 stone to capture all of the black stones.

Edit: Another way to imagine it is if neither player could pass. While yes White would lose territory as it played stones, it would be compensated by Black playing stones that will be captured in the end. Thus it becomes a wash, and thus why dead groups are auto-captured.