No, this is absolutely not true. This false claim is repeated over and over, but it is not true. Both convergence and divergence are rampant. And several other patterns, such as extreme conservation, that make no sense. Of course you can always say, “well evolution did it,” because evolution and CD are so flexible. But don’t then say the data fit the theory. They don’t. If you don’t believe me, take a look at Klassen, et. al., 1991, Figure 6, which shows the consistency index (CI) for a whole bunch of data sets that had been compiled in previous studies (data set = character data for a set of species).
The figure shows the CI value plotted as a function of the number of taxa in the data set. The CI values were consistently terrible. This was especially evident in the more meaningful studies, with greater #taxa. Above about 30, almost all the CI values were less then a half! They ranged from about 0.2-0.4, with random being around 0.15. In other words, the results were far closer to a randomized data set. This meta study incorporated a lot of data, and showed that you are usually closer to a randomized data set than anywhere close to the CD model.
Again, we all know that evolution and CD can do anything, but the claim that “common ancestry makes excellent sense” of the observations is simply false. You can always make Theory A fit Observations B; that doesn’t mean there an excellent fit. There isn’t in this case. This notion that the biological evidence just excellently fits evolution and common descent is simply a myth.