And in any case, why not use the R3T as the base?
One reason could be the end of the R3 line. While many have been asking for a real full fairing version of the R3T, its hard to imagine Triumph would develop a version of the Thunderbird so close to the R3T and let the two to compete for customers.
I don't think Triumph really wants to be in the cruiser business, but given the size of the cruiser market in the US they probably need they need something to compete. I also think they see the Thunderbird as the logical competitor to Harley and the clones.
The majority of their development in the past few years has been on their adventure and sport bikes. They have the Bonneville and related models for that market and currently 2 very different cruiser models. I don't know what their sales figures look like, but if new Thunderbird models start taking sales from the R3, I don't expect her to be around much longer.