you have a choice about what you do, but not about what you want to do.

This is demonstrably not quite true. Your wants change, and you have some influence over how they change. Stupid example: it is not difficult to make yourself want very much to take heroin, and many people do this although their purpose is not usually to make themselves want to take heroin. It is then possible but very difficult to make yourself stop wanting to take heroin, and some people manage to do it.

Sometimes achieving a goal is helped by modifying your other goals a bit. Which goals you modify in pursuit of which goals can change from time to time (the same person may respond favourably on different occasions to "If you want to stay healthy, you're going to have to do something about your constant urge to eat sweet things" and to "oh come on, forget your diet for a while and live a little!"). I don't think human motivations are well modelled as some kind of tree structure where it's only ever lower-level goals that get modified in the service of higher-level ones.

(Unless, again, you take the "highest level" to be what I would call one of the lowest levels, something like "obeying the laws of physics" or "having neurons' activations depend on those of neurons they're connected to in such-and-such a manner".)

And if you were to make an AI without this sort of flexibility, I bet that as its circumstances changed beyond what you'd anticipated it would most likely end up making decisions that would horrify you. You could try to avoid this by trying really hard to anticipate everything, but I wouldn't be terribly optimistic about how that would work out. Or you could try to avoid it by giving the system some ability to adjust its goals for some kind of reflective consistency in the light of whatever new information comes along.

The latter is what gets you the failure mode of AlphaGo becoming a poet (or, more worryingly, a totalitarian dictator). Of course AlphaGo itself will never do that; it isn't that kind of system, it doesn't have that kind of flexibility, and it doesn't need it. But I don't see how we can rule it out for future, more ambitious AI systems that aim at actual humanlike intelligence or better.