The Whole Truth

Systems where the person pleading guilty does not have to offer evidence of what they are saying are not very popular in democracies.

There is a similar-ish thing in Poland but I don't know how widely it's used or the details of it. You can formally ask to be punished right away. The prosecution must agree too and the court must find that what you said proves that you did what you claim you did. The upside is that it's quicker for you and you can try to get your punishment to be lower, the upside for the court and the police is that they don't have to do a lengthy procedure as they would if you tried to fight back. You also can't do it for crimes that are a "zbrodnia" ('fedolny, sort of, minimum 3 years in prison), just for ones that are defined as a "występek" ('offense', .. again, sort of).

AFAIK in most countries the plea bargain is not allowed as it is considered a violation of the accused's civil rights as well as a violation of justice.

Civil rights because of the inherent asymmetry of power (violation of the Geneva convention on torture since you're getting a confession, whether legitimate or not, under threat of force).

Violation of justice because if the person is found based on the evidence to be guilty then they should get the appropriate sentence; if not they should not. In theory the plea bargain is "clemency for taking responsibility and admitting guilt" -- in practice it of course is not. And someone who pleads guilty without a prior agreement will be at a disadvantage, again leading one to believe that the plea bargain case is for the innocent.