Not only does the US not care about justice, they favor the government, always. In a federal conviction you used to have forever to file an appeal, but that was determined too expensive (because people could utilize it) so they made it 10 days. But that was too short. So they made the fair compromise between 'an appeal should always be allowed' and 10 days, and made it 14 days for defendants (but 30 days for government because you know, the government has more limited resources than someone sentenced and being moved across country in prison transports between detention centers to their assigned prison).

Also a reminder that in order for a plea to be valid the defendant has to agree/swear on the record that they weren't coerced in anyway way into making the deal (because you can't waive your Constitutional right to trial under coercion). The threat of prosecution/a very harsh sentenced being reduced sure seems like coercion and that plea deals are constitutionally invalid by default.