I'm not sure plea bargaining is something that was inherited in that way, although of course many of the founding principles were retained - indeed, one of the founding objections in the Declaration of Independence was that the King was infringing the traditional legal protections afforded by the English legal system - a pattern which continues to this day, with governments here starting to infringe protection against double jeopardy which the US still holds to.
There are other systems out there - but I would say the choice made by Australia, Canada, the US and others to retain much of the English approach is a good one, particularly when I compare it to the others I have learned about. When followed, it's a good and robust system, the product of centuries of experience and refinement. Other aspects of the government are much less palatable of course: the lack of separation of legislative and executive functions in particular, and much less democracy and accountability than I see in most US states, but the actual legal system is a good one.