Since we are called to share the death of Jesus in some real way (being baptized into His death so we can rise again with Him, and a few other things along this line from the epistles), the real question shouldn’t be “Why did Jesus have to die to save us from X” (which ought to be primarily “…save us from our sins”, not “…save us from hell” or punishment or whatever, although that happens, too, as a consequence), but rather “Why do we have to die to be saved from our sins?”
The scope wouldn’t matter in principle either way: “Why did Jesus have to die to save all?” is no more a challenge in principle than “Why did Jesus have to die to save some?” But everyone who is saved from sin (however many that is) must share in the death of Christ eventually. And one way or another everyone does die: mortality is 100% total, even if there’s an instantaneous rapture coming for some people. Those people still wouldn’t escape dying (only the more annoying aspects of it), because they still must die to and in and with Christ.
That’s another main reason why I don’t accept the popular penal substitutionary theory, by the way: if Jesus merely substitutes Himself for our punishment of death, then there is less than no reason why we’re supposed to share Christ’s death with Him! It also breaks on the undisputed fact that those with whom Christ has already shared eonian life still end up dying, often very painfully and messily, after all.
I’ve written at length elsewhere why I accept a special variety of PSA (though not exclusive to some other atonement notions): Christ as the seed of Abraham acts in commitment to the covenant made by God with Abraham (which Paul regards as being actually a covenant between the Father and the Son since only God actually participated in the covenant, the Son on behalf of Abraham as Abraham’s seed) on behalf of all the children of Abraham who have failed to keep the covenant (which because Christ creates all creatures and incarnates as a descendant of Abraham means all rational creatures are through Christ reckoned as also being descendants of Abraham!) That covenant was to bring all the children of Abraham into the inheritance blessing, which Paul regards (rightly) as salvation from sin where through sin we have forfeited our rights as heirs. (This utterly destroys the whole notion of a Calvinistic elect, by the way, although Calvs are just as likely to try appealing to those scriptures for their position without realizing the implications of it. 
)
That in itself would be sufficient for why Jesus has to die, although innocent of sin Himself: He’s keeping His word to uphold the covenant to bring all rational creatures to salvation. But rebels against God must willingly join with Christ (sooner or later) in dying for the sake of the covenant: we cannot die on our own to keep the covenant because it is only by Christ that we would live at all afterward, so doing so would never be of benefit to us on our own. But more to the point, we cannot escape from rebellion by refusing to cooperate with God, which can only be more rebellion! – so if the Son dies we can either die in cooperation with Him, or refuse to do so (one way or another).
So what does it mean to die with Christ? 
That ought to be easier to work out.
(I talk about death from the perspective of the 2nd Person of God, in relation to God’s self-existence, the creation of not-God reality, sin, repentance, reconciliation, and the Incarnation and Passion, several times in SttH from Section Three onward. I don’t start in chapter 41, but I start pulling it all together there through the following chapters. I don’t talk about the Abrahamic covenant, partly because I didn’t know about it back in 2000 when I originally wrote it, or even a few years ago when I edited the 3rd Draft, but also I wouldn’t add it now because it requires a lot of scriptural discussion which that book isn’t really about. Even without the Abrahamic covenant aspect I still would expect the Son to voluntarily die at the hands of sinners in order to show us several things including how we ought to be cooperating with the Son.)
