Sorry you are wrong especially about your first example. For the other two yes there aren't built in toolboxes to handle those but it can be done. R has a lot of packages + it's a language so anyone can effectively write anything: https://cran.r-project.org/web/views/
I can write anything to do any computation in any programming language. The whole point is that there are pre-existing, high quality libraries and toolboxes to do these operations. In fact, that is exactly why R is popular - it has excellent libraries for handling data and statistics.
You're right. R does in fact have a library for modeling Kalman filters. My mistake! Let me pick any other example from the Matlab toolbox product list that R doesn't have! Can you model a radar system in R? Can you tune PID systems in R interactively? Don't be a pedant. Since you are familiar with R, you should know R is 95% used by data scientists and others involved in statistical work.
