If the societal cost of enforcement exceeds the societal cost of non-enforcement, then perhaps they should ignore the situation.
> or to find someone to hold accountable
This is why it would have to be decided by a judge as part of sentencing. If they're actually accountable then why shouldn't they be held to that?
> Just extend the logic to the other expenses of an investigation- hourly pay, overtime, materials, forensics. Making a criminal pay for their own arrest is a terrible idea.
I don't necessarily disagree, but just to play devil's advocate: why? It's their fault the public had to spend money on this, so why shouldn't they pay for it? (One argument I can think of is that for small crimes the cost of enforcement may greatly exceed the bounds of reasonable punishment for the offense, but what about when that's not the case?)
> Those things are not related to the crime itself
I'd argue exchanging gunfire with police is definitely a big part of the crime committed in this case. The shoplifting that started the encounter is practically irrelevant compared to that.