Avoiding Java's string footguns is an interesting problem in programming languages design.
The String.format() problem is most immediately a bad compiler and bad implementation, IMO. It's not difficult to special-case literal strings as the first argument, do parsing at compile time, and pass in a structured representation. The method could also do runtime caching. Even a very small LRU cache would fix a lot of common cases. At the very least they should let you make a formatter from a specific format string and reuse it, like you can with regexes, to explicitly opt into better performance.
But ultimately the string templates proposal should come back and fix this at the language level. Better syntax and guaranteed compile-time construction of the template. The language should help the developer do the fast thing.
String concatenation is a little trickier. In a JIT'ed language you have a lot of options for making a hierarchy of string implementations that optimize different usage patterns, and still be fast - and what you really want for concatenation is a RopeString, like JS VMs have, that simply references the other strings. The issue is that you don't want virtual calls for hot-path string method calls.
Java chose a single final class so all calls are direct. But they should have been able to have a very small sealed class hierarchy where most methods are final and directly callable, and the virtual methods for accessing storage are devirtualized in optimized methods that only ever see one or two classes through a call site.
To me, that's a small complexity cost to make common string patterns fast, instead of requiring StringBuilder.