Plea deals were illegal for the majority of America's history.

You could help fix this problem by removing the 'trial' tax. Currently you receive a much lower sentence if you take the plea. If a punishment is truly fair based on the crime the sentence should be required by law to be the same in both cases.

And are still illegal/unused in the vast majority of the rest of the world.

And in most of those jurisdictions where it is a possibility, its use is massively less (less than 1% per capita) and also far more regulated, and subject to review. In the US a judge ostensibly has the power of veto over a plea deal, though in practice this is nearly never exercised unless the miscarriage of justice (in either direction) is so egregious that it can't easily be ignored.