I think maybe you are neglecting game theory for the accused, its hard to
incentivize people to act in their collective interests, when they are
thinking of their own future freedom and lost earning capacity.  I imagine
you even have researched the statistics for this, but to summarise the game
theory scenario: plea bargaining clearly results in less accurate justice
(more innocent people do jail time), but has the real-politic benefit of
reducing the cost of implementing justice.  The usual pattern (made up
average numbers) is accept the plea do a discounted (lower than sentencing
guideline) 3 years, reject the plea, the prosecution will make less
reasonable/inflated charges (higher than sentencing guidelines, based on
more tenuous/unlikey to be provable charges) threatening a scary 30 years,
which in reality will be moderated down by a judge if the accused has the
money for a decent lawyer to 5 years, if they lose, or 0 years if they win;
if they are relying on an overworked, less capable public defender because
they dont have the money to buy proper representation, their chances of
winning are lower, and if they lose their post-trial sentencing will be
higher at 10 years.

Now law is a remarkably imprecise subject, especially when muddied with some
not-so-scrupulous and politically motivated prosecutors, police entrapment,
police bias (push for conviction based on opinion/bias, but statements given
disproportionate weight by a system that believes it's officers over the
public).  (Prosecutors and police are politically motivated because their
career depends on conviction rates, headlines).  The system seems to largely
ignore or not give adequate weight to investigating significant
prosecutorial abuse or police bias.  Prosecutorial abuse has to be strongly
proven, and the perpetrators are career ambitiuous, and legally qualified so
know the grey areas they can exploit where the abuse will be unprovable even
when it is very rarely alleged, or actually prosecuted.  Like police they
have the benefit of the doubt, in a judicial system that favors its own
officers, and so they are defacto largely immune from sanction from even
significant systemic abuse, unless stupid enough to be caught red handed
with with a smoking gun.  Which is to say even if you have millions to your
name for the most capable legal defense, and completely innocent with
reasonable but not iron clad alibi, its still subject to a high degree of
randomness depending on political motivations surrounding.

So therefore people will not fully follow game theory of going for the
lowest expected sentencing.  Ie if p is probabity of winning, and the
numbers above: then its 3 vs expected (p*0+(1-p)*5) so even p=2.5 its 2.5
expected vs 3, so if that was an investment you'd say good lets do it.  But
if its choice between 3years and no more stress, vs legal defense cost and
years of stress followed by 5 years if you're unlucky.  The dillema still
holds if the odds p=0.75 and you have lots of money I suspect sadly that
thats about as high as p gets for many areas of law.  You also have to
factor in the loss of income (at the average income for prisoners) into the
equation, and a premium because people would sooner earn less and have their
freedom.

You cant reform the system via kickstart fund and incentivize people to not
accept pleas, well not at $5k anyway, because they'd need compensation for
lost earnings and a huge loss of liberty premium if they lose, a stress
premium for going to trial, and expenses for high quality legal defense.
Those figures may no longer make game theory economic sense for society,
though I do think the centuries old principle that its more important for
one innocent party to go free than 100 guilty to be imprisoned is not
properly incorporated into the current system as plea bargaining removes
most of that intended objective.

Even with best attempts at fairness and balance from police, prosecutor and
judge (and there are genuine public spirited ethical people in some of those
roles, who would ignore the perverse career motivations on principle, so it
probably happens some of the time), the outcome STILL has an unfair plea
imbalance and STILL high randomness.  Its an imperfect system even under the
most favorable conditions.

I think the solution is to politically vote to arbitrarily cap the
incarceration rate to 10,000/annum; the justice system is not allowed to go
over that limit by law.  They will then focus on cases where they think the
incarceration is of most value to society (eg of making the public safer by
taking a violent criminal off the streets).  Maybe the cap should be
adjusted based on false conviction rates, if the false conviction rate
increases, the cap decreases.  Independent review of potential prosecutor
abuses should be increased.  Also the system should be restructured to
remove the career/political motivation for prosecutors to achieve high
conviction rates.  Their conviction rate should include a heavy mallus for a
false conviction, so they strive to avoid convicting innocent people, and
the system should somehow be adjusted to be less adversarial and to remove
sentencing penalties for going to trial.  eg Maybe the trial sentencing
level and charges should be set by an independent neutral body, not the
prosecutor, with the objective of keeping the trial and plea sentencing the
same.  Maybe simpler bargaining should be made illegal.

Another specific problem in the US is its a one dollar one vote system, and
operating privatized prisons is a high profit business.  The prison
operators votes therefore likely outweigh the proportion of the public that
is aware of the system problems or care enough to vote about it.  I believe
other eg european justice systems are in fact less prone to these issues.
So another solution is to vote with your feet.

Basically in such a system you want to avoid even interacting with the legal
system or justice system, period.  Even volutarily interacting as a random
by-stander is unfortunately likely to be net loss to your finances or even
freedoms.  Even to complain publicly about the defects of the system is
probably risky once you have interacted with them.  Which is ridiculous but
thats the reality.

And finally some of the laws on the books are ridiculous on their face in
the opinions of the accused's peers.  eg computer abuse act which sees Weev
in jail and such like stories, and the sentencing guidelines are also often
ridiculous and non-proportional eg the sentencing threats to Swartz for what
was probably not even a copyright crime (going on the theory from his
previous activism pattern that he was aiming to republish the subset of
articles that were public domain).  His trial sentencing threat was above a
1st degree homicide with iron clad evidence, something's got to be wrong
with that.  The sentencing board are failing in their task.  Something
should also be done to restrict scope for judicial vengence also - Swartz
made a mockery of a stupid law, with his previous popularly supported
activism stunt, and so prosecutors were out to get him.

Also legal systems generally seem to lag 50-200 years behind the opinions of
the public Some jurisdictions are better than others, but the system of case
law mixed with precedent creates a built in brake on legal theory evolution.
Out of touch with reality and public opinion prosecutors, judges and
sentencing another issue.  Probably law should be restricted to 1MByte of
ascii text and any law not approved by 90% referendum (1 person one vote,
not 1 dollar one vote) struck off automatically every year.

This state of significantly imperfect, and hard to reform, high cost legal
system issue is why smart-contracts look so attractive.  Its not even
obvious how to improve the legal systems and they evolve slowly and resist
experimental change.  Mathematical aprior enforcement, deference to mutually
agreed competing impartial arbitrators for dispute.  Pseudonymous
smart-contracting parties FTW.  Of course it doesnt work for in-person
crimes, except in a "Snow Crash" sense (cometing legal systems/governments
in the same physical space) but a justice system that leant heavily on
smart-contracts and refused as a principle to revise contracts where both
parties received competent legal advice, nor overturn arbitrator decisions,
would be a step forward for society.

Adam