He thinks [CP [C' 0 [IP they have read War and Peace. ] ] ]

because that choice allows us to give the same account of why constituents can be extracted out of the embedded clause as we give for the case where the complementizer is overt. Without the CP projection, extraction would result in a subjacency violation. An alternative would be to say that the IP is not a barrier when it is governed by a verb. This is what the text says about infinitival IPs and we could extend the stipulation to finite IP's as well. If we do, however, we predict that the following two sentences are equally grammatical:

Which book do you believe reviews of to have appeared last week?
Which book do you think reviews of appeared last week?

The judgments here are not as clear as one would like.

Another reason for preferring the standard analysis might be that English generally seems to allow silent complementizers (and even to require them when the Spec,CP position is filled:

the box (that) you lifted
She wondered what (*that) she should do.

All in all, these arguments are not as strong as one would like.