Hypothetically, your a law abiding diplomat traveling to a foreign land to discuss some negotiations. I am a resident of that foreign land but don't like your country or it's involvement in my country. To stop your countries involvement, I falsely claim that you committed a crime. If you can and are arrested, you can't complete your diplomatic mission.
If it's a theft crime,mabye. In cases of assault, sexual assault or anything involving a fatality, I don't think diplomatic immunity should protect the perpetrator. Maybe there would still be some penalty limits, but I think there needs to be an acknowledgement of the crime and some kind of atonement or reparation.
No, there are some crimes that are so awful that diplomatic immunity should not stand. Sure, something nonviolent or a crime based on a misunderstanding should have diplomatic immunity apply. But a serious crime where people are hurt and deaths result, well, that is a crime that should not be protected by immunity.
Unfortunately, the diplomats are more likely those who occasionally tend to misinterpret the extent of their privileges and thus make use or, to be more precise and correct, abuse their inviolability and immunity. Such abuses may still be tolerable by the receiving state in the name of securing effective performance of diplomatic functions, if these abuses involve merely minor offenses or crimes. But do receiving states and the international community have to tolerate personal inviolability and diplomatic immunity in case of serious crimes such as murder and conspiracy as well as war crimes and crimes against humanity?
While circumstances can always be taken into consideration, a criminal should not be able to hide behind diplomatic immunity for the worst of crimes. If the crime was not an act of State and if the crime is truly serious, then that person should be held to standards of basic human rights. If the criminal would be in trouble in his own country, why should he not be in trouble when he is abroad?