Just to add to Polama's response, the player shouldn't be able to kill important quest giver by mistake as it can and will lead to frustration. Imagine the NPC gives you quest to kill someone and your target runs just past your quest giver. You miss the target and there isn't anyone who could reward you later for that quest. But if you add a challenge to killing quest giver then it may be interesting.
Regarding your title question - ability to kill important NPC in not really freedom, it's game mechanic. Whenever you choose to implement it or not you should provide "things to do" for player. Be it quests, achievements, or just hints of what (s)he can do now or where to go. If you leave players with "what now?" question too early or too often they may get bored quickly.
You mentioned GTA, so let's get it as example. There is always at least one quest on your map where you can go. You may do hundreds of other things, but if you run out of ideas this the hint of what to do next. The same goes for Minecraft - basically game build around freedom that encourage you to do your stuff. But there are achievements that guide you in case you are not sure what to do.
well for the by mistake thing there will be somewhat of a warning "This game allows you to kill everybody so be careful with who you shoot at" and there could be some indication who are important and whose not there needs to be work rounds like giving those NPCs bodygaurds so it actually becomes a challenge and you choose whither you want to go through the challenge but you can do it if you have the right equipment actually this is why I am asking to know what would happen the pros and cons
I am saying freedom because of other games that restrict the player and change the rules when they feel like it