Because «хо́чется» is a subjectless verb, which works very much like «на́до». If you used «хо́чет», then «писа́тель» would be in the nominative case.

There's a very blurred line between treating the desire as something we can control, our action (therefore «я хо́чу») and as something that happens to us (therefore «мне хо́чется»).

Compare English 'I think' and 'it seems to me' (and archaic 'me thinks') — both mean roughly the same thing, but in the first case it's described as our action and in the second it's described as something that happens to us.