There's a world of difference between someone in your car when it's empty and someone in your home when you are.
No, in the car scenario, you and the intruder are both present together in the parking lot or wherever -- just as in the OP's home scenario. I only included the car to meet OP's criterion that the other person has already disregarded the law.
In public I have to be alert to protect myself, but if someone comes into my place of security and I don't have any way of knowing what they want, disabling them before they can hurt me or my family is the right choice.
Please explain. How do I have any more way of knowing what they want if I'm outside than I do at home? Why am I not also "supposed to be safe to do as I please" if I'm in public?
Any other choice suggests the intruder's interests supersede mine.
Nonsense. You and the intruder can each have rights that ought to be protected -- especially the right to live -- and you are ignoring an incredibly vast amount of of middle ground in between killing someone and having them kill you. For instance, in the absence of any clearly imminent threat, you can show your gun and give a verbal warning that you will use it if necessary.
Most or all Castle Doctrine laws include some version of a "reasonable belief" clause where the shooter
And you're more or less right, if there were a freeze gun this would be moot. But there isn't. So it isn't.
You're dismissing this part of the argument with insufficient justification. First, if we agree that lethal force is simply one practical means to incapacitation rather than an absolute moral right, then OP must qualify his conclusion in a number of ways.
Second, once you've acknowledged that lethal force is just a practical means rather than an absolute right, we've got to establish just how practical and effective an alternative option has to be in order to justify killing. All you've suggested is that "tasers are not foolproof," but that's an unreasonable standard -- nothing is foolproof, not even deadly firearms. If I am in an area where legal possession of a powerful projectile stun gun is legal (which is most cities in the vast majority of states), and I still justified in resorting to lethal force just because I chose to buy a handgun instead? If the stun gun is not effective enough, just how effective does it need to be in order for lethal force to not be presumed justifiable? You're admitting that there is a line somewhere, but ignoring the questions of where that line is, and precisely why you believe we haven't already crossed it.
Third, lots of state laws across the country distinguish between the use of deadly and non-deadly force and with varying versions of a "reasonable belief of imminent peril" clause. You might think these are trivial concerns, but in fact these are precisely the questions that actually come up when self-defense and Castle Doctrine laws are crafted.