At the time (~2002?), I think Java was a very reasonable choice for an cross-platform IDE. As more programming language research and different programming paradigms continue to gain mainstream adoption, Java's emphasis on backwards compatibility and stability makes it a bit difficult to change some of the initial design decisions that Java started out. However, since Java is so mature with an even more mature eco-system and an incredible runtime specification (JVM), it made sense to build a modern day "blue collar" language that could be classified as "Java, if it started out today." With that in mind, and some of the same principles that Java was founded on, Kotlin delivers on this promise. IMHO, it is the only JVM language that really does bridge this gap.

They didn't have to - JetBrains has been around for a long time and Kotlin is new. The productivity benefits mostly come from things like fast compile times, garbage collection etc.