Aren't MBTI and Big 5 connected?
All personality models are related in that they are carving up the same variance into different factors, and some of the factors will overlap. Extraversion is probably the most similar trait between the two models, but it's still quite different.

As a personality psychologist, I would say yes, this is potentially an overestimation of their convergence. A brief description of why the Big Five is preferred over MBTI is that the measures of the former are dimensional rather than categorical, have more test re-test stability, and have more stable relationships with other levels of analysis (e.g., genes predicting traits; traits predicting behaviors). Reliability and validity are the cornerstones of quality measurement.