Shoud you be able to buy your way out of jail time?

[Emsworth]

No

[Emsworth]

Maybe we could leave it up to the victim?

That would undermine the whole basis of the criminal justice system. Settlements are appropriate in civil cases, as a tort is deemed to harm just the defendant. However, a crime is an offense not only against the victim, but also an offense against society, against the People. Thus, victims should not be able to determine the sentences of criminals.

[Emsworth]

I'd like to see a philosophical justification of that.
How is it an offense against me that some guy in teh otehr end of the country pickpockets someone.
And don't use hipotheticals, as they are worthless.

It is not a philosophical argument, but an assumption of the law. The entity in which ultimate sovereignty and power is vested is the one against whom the crime is committed. Under the common law, for instance, a crime is an offense against The Crown, the ultimate repository of power. Similarly, in the U.S., a crime is assumed to be an offense against the People. The issue is not philosophical, but legal.

[Emsworth]

Actually, no. in primitive anglo-saxon common law, there were no offenses against magican entities like "The People" or "The Crown", as suits, even criminal, were among several parts, and the punishment was usually restitution.
What happened was when the Norman kings started to change the saxonic laws.

The U.S. legal system derives from the system implemented by the Normans, not that of the Saxons.