At the end of the day, while a Department of Justice and court roleplay can provide very enjoyable and engaging stories and enforces accountability for your actions (civilian or police), the flaw is that punishments for crimes are normally very minor. No matter what kind of crimes you commit, you only end up serving a couple of hours in prison.
In a real life situation, if the police have a warrant for your arrest or a valid reason based on probable cause or reasonable suspicion they can arrest and detain you for 72 hours without filing charges. Obviously we're not trying to perfectly emulate real life and the LSPD aren't going to hold somebody without charges for an extended period of time; after placing the charges you are immediately sent to prison.
If a court system were in place then it would be necessary to have a judge, criminal defence lawyer, and police prosecutor available at the time of arrest in order to have a trial. In the event that one of these are not available, a court date would need to be organised and then a decision would need to be made on the suspect.
Depending on the suspect and their alleged crimes, it may be acceptable to release them on bail. While released on bail they may be required to avoid contact with certain people, stay away from certain locations, and check in with police.
If the suspect has committed a serious offence, has previously broken the terms of bail, been convicted of a serious felony, are unlikely to turn up for court, or are likely to commit a crime while on bail then they cannot be released on bail. At this point does the suspect serve a full sentence, get released after a couple of hours, then go to court in a few days?
If a judge determines that the suspect is innocent, but they have already been fined and served time in prison, will the LSPD be responsible for reimbursing the fine on top of a payment for false imprisonment?
If the suspect is deemed guilty, will they just be released due to time served or is there extra fines and imprisonment added on top?
There is also the consideration of having and selecting members of the jury, which is very difficult when there are so many criminals on the server.