on the suggestion to "fix" the notoriety on getting killed/jailed, will not really solve any issue. It is meant to be a consequence for player to adapt and deal with. If anyone at will could remove this to escape the repercussion of its own actions will make the system mostly useless. before notoriety, you could simply buy a cheap sidewinder and suicide by cop to clear your name.... and you could now get back into your much more expensive killing machine to start killing innocents again...
There are plenty of things to say about the current Crime and Punishment system. of which the notoriety not so bad, it is one the most straight forward consequences in there. you kill a clean ship, you get tagged as the brutal criminal you should be classified as, ie we add +1 notoriety to your name. And you have to prove that you have learned your lesson, ie serving your time, ie waiting the required amount of time in game to clear you status, and if you keep on killing clean ships, we keep on piling up what that notoriety status, so you have to spend even more time to be a nice citizen of the galaxy, to clear your name. And there is no shortcut to avoid this.
And most importantly, you can still play the game, sure, visiting your home base, is more problematic, but you did do the crime, so now you do the time.
And I do not think the ingame options to deal with this is lacking, but the ingame information about the system is lacking...