A postcard from Chris Ambidge, with a lovely quotation from a May 31, 1811 letter of Jane Austen’s:
Letting her correspondent down gently: rather than asserting baldly that the mulberry trees are not alive (or even more baldy, that they are dead), Austen merely appears to be reporting her mental state about the matter, her fears. Nevertheless, afraid with a complement clause is often used to convey the content of the complement clause; the hedging with afraid in such cases is a matter of politeness, rather than truth value. Which understanding is intended is something you have to work out from the context.
Afraid has an entry in MWDEU, because of usage advice against it. On p. 44:
Bierce 1909 directs us flatly, “Do not say ‘I am afraid it will rain.’ Say, I fear that it will rain.” End of direction. Viztelly 1920 cannot find any reason for this proscription; Utter 1916 opines that the objection seems to be based on the theory that an adjective cannot take a dependent clause. Utter says that this “construction has long been good English,” even though the censorious condemn it as colloquial. Among the censorious must be listed Krapp 1927, who calls it colloquial.
The element of fear in Bierce’s example is not strong, a fact that makes his revision seem less than sensible. In Utter’s (I’m afraid I can’t go) and Krapp’s (I’m afraid you’ll have to wait for the next train) examples, it is even weaker.
MWDEU goes on to cite such uses of afraid “in impeccable literary sources”, from Shakespeare on, including of course Jane Austen (in Pride and Prejudice).
For me, the stylistic values of fear and be afraid with finite complements are shifted from the values discerned by some usage writers 50-100 years ago. For them, fear is neutral, be afraid informal or colloquial, but for me, fear is decidedly formal, maybe a bit old-fashioned, be afraid neutral.