I reckon it’s because they are usually little different to a GP once you have even a moderate number of evaluations, and require additional implantation effort.
What did you think of @andrewgwils paper that discuss the matter?
“t-process is useful where there are changes in covariance structure, or in applications such as Bayesian optimisation, where accurate predictive covariances are critical”
https://www.cs.cmu.edu/~andrewgw/tprocess.pdf …
to 
