I have great respect for Robinson's approach. I think it is very careful and reasoned. It recognizes problems with the textual evidence for some readings in the TR, while not throwing the baby out with the bathwater in rejecting the vast majority of well-used and attested manuscripts. It errs on the side of caution.
I think Robinson is right that the approach in the CT, while rigorous, can end up with a Frankenstein reading, where multiple readings are combined such that there is no known natural way of transmission in which they could have arisen. Vaticanus and Sinaiticus are important but they don't always even agree with each other and shouldn't be weighted too strongly.
The TR has the problem that one must, at least at some readings, give up on trying to point at manuscript evidence and just take it on faith. It is inconsistent to claim manuscript evidence in support of some sections and excuse the lack of evidence in others. If it's going to be an a priori conclusion that the TR is correct, then it's a faith statement (nothing necessarily wrong with that, but it's not consistently manuscript-based).
So I think Robinson's is a very balanced approach that I wish would gain more traction, but also point out that I truly do not have a problem using a Bible translated from any of those textual bases: the differences are providentially very minor and textual criticism is hard. The transmission of the biblical text is messier than we'd like.