Halliday & Matthiessen (2014: 270n):
Note that sequences of ‘verb: be + adjective + verb’ such as be eager to do, be keen to do, be willing to do are interpreted as verbal group complexes, as in she was terribly keen to get out of London. Note that unlike adjectives serving as Epithet/Head in nominal groups functioning as Attribute, these adjectives cannot be expanded with nouns serving as Thing/Head; contrast he is keen : he is a keen fellow, which is fine, with he is keen to finish the job : he is a keen fellow to finish the job, which does not seem possible. Note also the pattern of ellipsis: he is keen to do it, but he isn’t able to [Ø: do it].