The “good things” are the result of a close relationship with God, something God has to offer. It’s not a purely mechanical process of inheriting whatever spiritual status our immediate forebears had. God does offer that relationship, but chooses to do so on an individual basis.
Note that we also don’t directly inherit the spiritual state of a particularly depraved or vice-ridden ancestor. We all get the same deal – a will and intellect that don’t always control our passions and appetites, plus the offer of God’s grace to strengthen the one against the other. Our First Parents got a better deal, sure, but they still screwed it up and God is under no obligation to keep dispensing His grace the same way.
It is the “happy fault” not because it was not evil and destructive (it was, calling for the sacrifice of God Himself to illustrate its gravity and His response to it), but because our subsequent situation – with concupiscence but also with the option to become adopted children of God and spend eternity in His unveiled presence – is actually a greater destiny than Adam and Eve’s “live immortal earthly lives with a close relationship with God but not the Beatific Vision.” A fallen but redeemed and glorified humanity is a higher thing even than unfallen humanity.
No one inherits guilt for the first sin. We inherit a broken and deprived state, yes, but not moral fault.
It’s true that, without sanctifying grace supplied by God (whether through the ordinary means of baptism or by some extraordinary exercise of His mercy), even a human innocent of personal sin cannot enter Heaven. However, with only a few exceptions (such as the rather pessimistic St. Augustine), theologians do not generally consign infants to eternal suffering. They may technically be in Hell because that’s the only permanent alternative to Heaven, but we have always realized that it would be unjust to punish them as “proper” mortal sinners are punished, and God is not unjust.
The thing is, God hasn’t revealed to us what happens to such children, so we have had to hypothesize over the millennia, taking into account that baptism is the only definite means revealed to us for receiving sanctifying grace the first time. As others point out, those hypotheses have gotten ever more generous over time, increasingly recognizing that God is perfectly merciful and loving and isn’t going to lose a soul just because we couldn’t baptize someone before death. Thus the speculation has moved from lesser punishment in Hell, to existence in a very pleasant “top layer” of Hell (Limbo) that is Hell only in the sense that it is not Heaven, to the current “God can save whom He wills regardless of the rules He gives us, so entrust them to His mercy.” We only stop short of outright saying they all go to Heaven because God has revealed no such thing and there must be some reason baptism of infants is important. (Oddly, some Protestants who are totally okay with assigning any and every adult non-Christian to Hell do make that leap and assert that all children below a certain age go to Heaven, even though that really doesn’t seem to fit with their idea of how Original Sin and “the sin nature” work. I do not speak of all Protestant groups, of course.)