What you're talking about is an isolated system. I have an extended treatise on it here. In an isolated system, "the first ground fault is free" (and becomes the neutral-ground bond). This is the idea you are promoting.
The problem is the second one. Unless you have maintenance staff actively doing isolation testing and chasing down and eliminating that first ground fault, it will fail silently, undetected, and lay in wait. So you're right back in the same predicament, only now, you have no idea whether hot or neutral will be lethal to you today.
There is also the fallacy that you have discovered one use-case where your idea is better, but you're failing to consider all the other use-cases. The NFPA does, and considers them all in balance, and develops best practices that will save the most lives and houses. That is literally their job, being the National Fire Prevention Association.
Also an isolated system doesn't work unless you have your own transformer, because the entire system must be under common maintenance so you can assure it remains isolated. I have the luxury of having my own transformer. I have run it as an "isolated system" by accident (faulty neutral-ground bond). The "first ground fault" indeed failed silently and caught me unawares. I discovered this after de-energizing a circuit and pulling the wires off an outlet. I flashed hot to earth just to make sure the circuit was off, and this re-lit the circuit! What??? Turns out on an unrelated circuit, hot had faulted to ground. Ground was 120V from neutral everywhere in the system even on circuits which were turned off! That's super bad, and just the kind of nonsense that happens on isolated systems that aren't competently maintained. Failing silent is BAD.
I will say this: it was a good validation test for the previous work, which was a complete rewiring of a site which had dozens of serious defects.