If you want a static type system that is sound and decidable, it will necessarily reject some programs that would behave just fine at runtime. That’s not really Gödel’s fault. It follows more directly from the halting problem.
But that's a quibble, and I still know what to make of your stance. The thing you're not okay with is having the system "get in your way", which is your false positive (the polarity doesn't matter, if that's what I'm getting wrong). The point is you want to say "my program is correct, now run it for me", and you will hate if the system rejects it.
What you don't hate is runtime type errors.
There is no judgement on my side on the preferences. But I'm confused. If you don't have any static type checking, then it's like having a system that always gives negatives, and some of those will be false (again, assuming I got the polarity right. if not, just swap here and earlier). I'm pretty sure you're okay with this, even though the text of your last message leads me to believe otherwise.
To summarize, there’s a fundamental trade-off:
- If you want a sound type system (never accepts unsafe programs),
- And you want it to be decidable (terminates on all inputs),
- Then it must reject some safe programs.
If you're not okay with that, then... sorry :D