What use is making your own interpreter. Also, it says platform independence. After all the degree of platform independence is limited by what all platforms your interpreter can run on. So, I don't see any advantage.
Well, you write your interpreter using a language that already exists. So if you choose one that runs on may platforms (like, say, Python), then on any of those platforms someone can get your interpreter and use it. So, for example, if you write your interpreter on Windows I can run that same interpreter on Linux and it will continue to work.
However, if you had written a compiler, you yourself would have to write the code generator for each platform. So, for example, if you wrote your compiler so that it worked fine for you on Windows, when I try to run it on Linux it generates code for Windows, not Linux, so it won't work. You would need to do extra work, adding a code generator for Linux, before I could use it.
Also, I dont know even one good use of dynamic typing. It is useless I feel. Of course, I am wrong, because there are so many dynamically typed languages out there.
I think dynamic languages are popular for two reasons.
First, they are easier to write. Type systems require extra work to get right.
Second, because dynamic language users don't need to understand a (static) type system, many people find dynamic languages easier to use. So many people prefer them.
Also, the theory behind typed languages has really improved over the last decade. They are much more flexible and powerful. So older typed languages are less flexible and typed languages in general still have a reputation for being rigid.