You are baffled by the western concept of justice.

In western philosophy an offender is considered to have offended against society even if their crime is of a personal nature. As such, they are tried, condemned, and punished by society according to codified rules. A victim, if there is one, is not really a part of this process.

There is a fundamentally sound basis for this philosophy, including equity (different justice for different people is no justice for anyone), impartiality, and respect for human rights.

There are other philosophies of justice: for example, the traditional "I'm strongest I get the best stuff" or "you dissed me ima kill you." Some are codified similarly to western justice ("killing a man is requires you pay his heirs 100 she-camels of which 40 must be pregnant, killing a woman is half that, killing a Jew one-third, and so on"). Others involve negotiation between victim (or their families) and offender -- which often works out well, since the offender is often is a position of power to start with and is very likely come out on top.

The simple "an eye for an eye" is just the beginning of a very very deep rabbit hole you can go down on the road to enlightenment.

I think you're confusing or conflating civil and criminal courts. If someone breaks a law, that's generally a matter for the state to decide in a criminal court. If someone was damaged (i.e. if the victim feels the perpetrator owes them compensation), that's a matter for them to bring up themselves in the civil courts. These are separate functions; one situation could be tried in both courts. A famous example off the top of my head is that even though OJ Simpson wasn't criminally convicted of murder of Nicole Brown and Ronald Goldman, a civil court found him liable, awarding tens of millions of dollars in damages, to be paid to their families.

Distancing the victim from the outcome of sentencing is by design and, arguably, for the better in a democracy. Crimes violate the social order, not just the victim. It behooves us all to have a system wherein (in theory) the system, not the victim, applies a set of rules to determine punishment, as contrary as that might seem to one’s sense of self, morals, etc. It’s a part of why “justice is blind.”

I strongly disagree. The victim is generally deeply incapable of being objective about the situation. How many perpetrators of domestic violence would go free because their spouse is too scared to ask for proper punishment? This is already a big problem with securing cooperation for prosecution, and I'd aim to make that better, not worse. You'd have enormous disparities in sentencing based on the personality of the victim. Should mugging a vindictive asshole carry a harsher sentence than mugging a nice person who believes in second chances no matter what?

The justice system is pretty far from actual justice in many cases, but this wouldn't get it closer.

There are (institutional, complicated, well-ordered) civil and criminal systems elsewhere in the world where victims are much more directly involved in sentencing and punishment, and you probably wouldn't want to live in one.

Most criminals aren't in a financial position to pay compensation. And even if you get a judgment, good luck ever collecting. When a drunk driver damaged some of my property I didn't bother sueing him because he was obviously a worthless deadbeat.

In most US jurisdictions the victim of a crime is allowed to make a statement during the sentencing phase of the trial. So the victim can certainly request release if they want it although the judge isn't obligated to adhere.