i think what dundas--goodwillie--mccarthy are getting at on page 125 is the following.
1. their foundational choice of using Gamma-spaces to model connective spectra means that they can't make this cyclic bar complex definition directly, i.e. without cofibrant replacement.
2. they don't see how to get the cyclotomic structure from such a cyclic bar construction, anyways.
their way of solving these problems is to use bokstedt's alternative (but equivalent) model for THH. personally i always found this definition pretty conceptually opaque, and i think a major advantage of the nikolaus--scho…