If a defendant wants to skip the trial and admit guilt, that's a different matter.
A fair trial is not a purpose, it's a means to an end (punishing people fairly). It is not even a necessary component. The only reason it exists at all is because of our inability to objectively determine guilt in most cases. The rest are tacked on (IE determinations of what crime has been committed. Even this would be solved if you could objectively determine what occurred)
However, again, if the defendant admits guilt (even if not in public), but still wants a trial, can you explain how the system is served by a fair trial on guilt or innocence for him, rather than a fair sentencing hearing?
In that case, the guilt or innocence is not in question. The same is true when they only admit guilt to a defense attorney. Defending the client, and trying to get them off during the trial stage, does not serve the ends of the system. It may, depending on how formulated, serve some of the means, but that's kind of irrelevant.
The system is best served by not being allowed to randomly put whomever in jail for whatever [1]. So we would require the prosecution present legally-obtained evidence that the defendant has committed a crime to establish that fact. Defence attorneys are to ensure that there is a fair fight because we cannot expect all of the accused to be legally savvy. To make this effective, the defence must be able to speak to them in confidence, ergo attorney-client privilege. So the defendant admits to his lawyer that he killed a woman. If the state is overreaching on charges, let's say murder one when he did it on a whim, he actually should not be convicted of it. Giving a good defence is supposed to ensure that when an accused is convicted they are convicted beyond a reasonable doubt. "Better one thousand guilty walk free..."
Also in that case the defence would likely advise the culprit to admit guilt to a second or third-degree murder.
[1] Although I don't think it's succeeding very well at this due to overreach by the states as far as charging too much to get a plea bargain.
They aren't randomly putting whomeever. They are putting a guy who admitted to a crime, and is in fact, guilty, in jail. And not even in jail. My only objection was to the trial, not a sentencing hearing. They are welcome to argue whatever factors/mitigations/excuses they want at that hearing.
You still haven't answered what the trial buys you there.
The rest is a discussion about why we have an adversarial system for the case where guilt is not objectively known. I don't at all disagree with that part (though i agree both sides are blameworthy for various things and in various ways).
IE "Giving a good defence is supposed to ensure that when an accused is convicted they are convicted beyond a reasonable doubt."
But he admitted he did it, and actually did it. You objectively know they did it. The "reasonable doubt" standard is a subjective standard, which is standing in for the lack of objective knowledge. Here, we have that objective knowledge. So what exactly is the subjective standard buying you in that case, and why does that serve the end goal, rather than the current means, of the system.
Notice that this is one approach, the traditional (dare I say right wing?) one. It's exemplified in the Saudi's punishment of cutting off thieves hands. OTOH, it's mostly rejected in Europe, where justice is supposed to rehabilitate, not punish. That's why there isn't death penalty, and why there are notoriously comfortable prisons; "justice as punishment" is seen there mostly as backwards and barbaric (probably because of all these socialists there :). has