Pure functions excel at state management and reducing bugs. If there were a reason to make games with a functional language, this is the reason.
The big issues seem to be deterministic performance and resource usage. Garbage collection, lazy evaluation, etc all result in bubbles of weird performance. That doesn’t matter for the overwhelming majority of programs where the human limits in responsiveness is hundreds of milliseconds, but does matter it must scale into single digit milliseconds.
There are functional languages that have this capability, but outside of the partially functional Rust, they are basically unknown.