Yeah I realise that getting rid of the permanent heap allocations won't make a big difference, it's somewhere to start though in getting tighter control over the heap.
There are deletions when 'String' objects get deleted so I might write my own String class that uses static buffers.
There once was a time in the recent past where what you are suggesting would have brought cheers from all in the forum especially the Uno folks.
But times have changed, memory resources have increased, and the ARM uC's such as the Due are 32-bit beasts with very clever compiler.
Arduino15/packages/arduino/tools/arm-none-eabi-gcc/
I have worked extensively with the STM 32-bit hardware lots and dynamic allocation has not posed any issues. My experience, others here may have a different story to tell.
I agree with aarg, but if you have spare time for the rewrite, go for it but you are taking ownership for the code your x-coworker wrote and after rewrite, you have no one to blame
And if the existing code creates no issue then your time might be better spent on something else (and definitely not rewriting yet another String library…)