Exactly. The "right to an attorney" is actually intended to be a check on government power and it's not an economic entitlement like food stamps. One can see in the Declaration of Independence that the complaints included a "right to a speedy trial" and "right to a trial by jury" because the monarchy government was abusing its power and throwing people in prison on arbitrary whims. That's where the right to have an attorney came from. We should note that the USA does not provide government-funded lawyers for suing your landlord, incorporating your company, or filing your patent application. (Maybe the government should but that's a different conversation.)
If the government is the adversary in criminal prosecution and they can take a citizen's life & liberty away via prison sentence or capital punishment, that is the limited case where the government will provide an attorney. When the government is the opponent in other departments such as the IRS disputing taxes owed, or SEC investigating financial disclosures, there is no "right to an attorney" in those cases to help the citizen fight them in court -- unless it turns into a criminal prosecution.
I also hesitate to describe any right at a check on power. That suggests planning, an overall design. There is no grand master plan. We have a series of rights rooted in history and tradition. Religion has played a large part. The system has never been designed. Even the founders writing of the constitution was really just a tweeking of some longstanding ideas.
The percieved "balance" is fiction. Other countries have very different rights and do not tip into chaos. Canada lacks the right to a jury trial, and yet somehow isnt a lawless dictatorship. The UK has a very different concept of free speech, yet the BBC is probably the most trusted source of news on the planet. Other systems work, perhaps better.
I suppose you don't consider a sort of grand, overarching code of laws, as constituting any sort of plan? And if there was a plan, would you imagine that there would be sort type of foundational precepts of that plan - a sort of legal "constitution," as it were? And if there was any type of plan, do you think there would be any group of people, or maybe men specifically (if it were a centuries old plan), who founded it?
The claim isn't that the constitution was wholly novel out the time, or that it is the only type of legal system that can (or even necessarily does) lead to a long running stable government. The claim isn't that the plan is immutable, or tightly controlled by a singular central authority. The claim is just that the US legal system was, literally, planned.
Arguging that the BBC (or really any singular news source in 2018) is "probably the most trusted source of news on the planet" is a hyper-contentious claim. And this is the UK's "freedom of speech" -
Article 10: Freedom of expression
1. Everyone has the right to freedom of expression. This right shall include freedom to hold opinions and to receive and impart information and ideas without interference by public authority and regardless of frontiers. This Article shall not prevent States from requiring the licensing of broadcasting, television or cinema enterprises.
2. The exercise of these freedoms, since it carries with it duties and responsibilities, may be subject to such formalities, conditions, restrictions or penalties as are prescribed by law and are necessary in a democratic society, in the interests of national security, territorial disorder or crime, for the protection of health or morals, for the protection of the reputation or rights of others, for preventing the disclosure of information received in confidence, or for maintaining the authority and impartiality of the judiciary.
edit: added and emphasized that the UK's freedom of expression is not a foundational part of UK law
Fix: Allow people to sell, or sell shares in, their right to sue.
The fact that this is not more popular suggests that litigation is not efficient for the rich, either. In the end it only enriches the lawyers.
[0] https://en.m.wikipedia.org/wiki/Legal_financing [1] https://news.ycombinator.com/item?id=15249825
"You have the right to have an attorney. If you cannot afford one, one will be appointed to you by the court." is the language intended to be used in the Miranda warning; and it is not so much that you have a right to an attorney, but that your right to a speedy and public trial (...and to have the Assistance of Counsel for [your] defence) combines with the state's mandate to prosecute your case to produce a mandate to provide you an attorney.
The "right to an attorney" is a colloquialism for referring to the state's obligation to fulfill the requirements of a constitutional trial if they want to try at all, which in practice either means the state hires public defenders, or the state can not try you (though this wasn't done in practice until it was interpreted this way in court).
There are other legal colloquialisms such as "jury nullification", which is an emergent behaviour rather than an explicit one.
Guess we'd better scrap that whole "right to an attorney" portion of due process, then.