The problem with that is often times "codifying" things with government regulations ends with several orders of magnitude of unintended consequences that often do not improve the lives of the people you are targeting while at the same time making the lives of everyone that do not have the problem today worse by creating similar or other problems for them
Could this happen? Yes. Would it happen? Highly unlikely. Not for something as simple as changing the laws to require a reason and evidence to fire someone.
Now then, a more likely complication would be riders. But that's not a side effect of codifying employment termination requirements, that's a side effect of shitty legislators.
And that? We have some control over that.
And again, we're not talking about some new legislation with no prior art. It's how it was before the at-will laws came into play, it's how it still is in some states, it's how a large number of companies work today and it's how it is in a majority of other developed nations.
The problem here is you state clearly that a "clean bill" would be impossible yet you want to argue the issue like a clean bill was possible.
Sorry reality does not work that way, any attempts to change the law would have massive side effects because the "riders" as you call them would be added, the bill would not be a 10 page ensure employers go through a PIP, no it would be a 1000 page grab bag of special interest back room deals