They're just "assassinations"... all assassinations are targeted.
are a reality of political and military life
For most world states - they are not. They have an absolutely dreadful effect on the potential of amicable resolution of conflicts, because not only are they a hostile/belligerent act in themselves, but their effects on the attitudes of political leaders and the populace of the country in which the assassination was carried out is extremely negative.
When state A targets state B with an assassination (assuming it is not both clandestine and easily attributable to a third party, which is another kettle of fish) - almost the only way state A can get state B to later accept its requests or expectations on various matters is through the surrender and submission of B. So, if I look at assassinations by states today, I see them in situations of strong imbalances of power: US vs Iran, Israel vs the Palestinians, to a lesser extent US vs Russia. For other state pairs, this is not a reality of life.
and perhaps an unavoidable necessity when it comes to national security.
As it is not an option for most states, obviously it's quite avoidable. But the US defines its "national security" as more-or-less world hegemony, and when that's the case, who's to say what's unavoidable.
Yet, in my understanding it does not square with the western values:
extrajudicial punishment (no due process),
This is a never-ending struggle, mostly internal and also external to states. Without significant, constant, public push-back against state institutions, due process rights get eroded, or not introduced when they are missing. In particular, w.r.t. the US, there is very little due process tradition preventing you from getting shot by law enforcement: US police kill well over 1,000 (maybe 2,000?) people annually without having been attacked, with no process whatsoever.
violation of other country sovereignty
Since when is that a western value? This has been the favorite pastime of European powers and the US for centuries. Not that other world states aren't guilty of this as well, but - come on. Actually, IMNSHO, the whole notion of sovereignty is historically a powerful minority getting control over an area and its residents and sanctifying the legitimacy of that act and its consequences.
in some cases violence against its own citizens
We could argue about this, but - Zawahiri is not a US citizen; nor would it have helped him, as even a citizen like Anwar Al-Awlaki was assassinated in Yemen by the US and there wasn't even a public outcry, let alone criminal and impeachment proceedings. After all, such people are not "one of us", the perceived group worthy of procedural protections.
In this sense, the US president openly claiming personal responsibility for a killing looks somewhat unsavory.
Don't you remember that US presidents, at least since Obama, have a "kill list" which they sign off on, weekly or otherwise routinely?
See the Disposition Matrix Wikipedia page and references therein.
What is the rationale for this US policy?
Well, I would say that the political culture in the US seems to be gradually moving towards unfettering the top echelons of government of even the semblance of the same legal and moral requirements normatively applied to individuals or non-privileged organizations. This is perhaps ironic, as the US has historically touted this not being the case as one of the attractive features of its regime, and aspect of the people's liberty, but - well, the times they are a-changin'.