I believe you are proposing a language-based security (langsec), which seemed very promising at first but the current consensus is that it still has to be accompanied with other measures. One big reason is that virtually no practical language implementation is fully specified.
As an example, let's say that we only have fixed-size integer variables and simple functions with no other control constructs. Integers wrap around and division by zero yields zero, so no integer operation can trap. So it should be easy to check for the infinite recursion and declare that the program would never trap otherwise, right? No! A large enough number of nested but otherwise distinct function calls would eventually overflow the stack and cause a trap or anything else. But this notion of "stack" is highly specific to the implementation, so the provable safety essentially implies that you have formalized all such implementation-specific notions in advance. Possible but extremely difficult in practice.
The "verifier and runtime sandbox" mentioned here is one solution to get around this difficulty. Instead of being able to understand the full language, the verifier is only able to understand a very reduced subset and the compiler is expected (but not guaranteed) to return something that would pass the verifier. A complex enough verifier would be able to guarantee that it is safe to execute even without a sandbox, but a verifier combined with a runtime sandbox is much simpler and more practical.
