There's always a trade-off between performance and security, but with better tooling support the price for secure code will be very low. Right now security is bad because we look at security as a feature. As something that is added to a project, instead of as something that guides the entire design.
Your suggestion that static analysis can fix this is wildly optimistic, because C/C++ code for a modern browser uses memory pools, pointer arithmetic, just-in-time compilation, and shared memory between object instances, threads and processes and so on. It's hugely complex, and correctness can't be verified with some sort of static analyzer or with added runtime checks.