God, indeed, does all of these things for His covenant people. For those who are not believers in Jesus Christ, God is under no obligation to do anything other than those things which He does as part of common grace.
God is not "under obligation" to do anything.
He drove Adam and Eve from the garden after they sinned, but he also made them clothes from animal skins. He did not give up with them and destroy them. He punished, forgave and restored the Israelites again and again after their disobedience - he didn't have to do any of that.
To put that into perspective for you, the vast majority of mankind are lost and will be lost eternally simply because they do not (and cannot) believe in Jesus Christ.
They are lost, certainly. Whether they will be eternally lost after they die depends on how God judges them.
If someone has never heard the Gospel, I do not believe God will judge unfavourably or condemn them. Likewise, if they "cannot" believe. God knows their hearts and whether or not they have truly been given a chance to accept his Son.
And no, I'm not a universalist. I just don't believe God will punish someone who has genuinely not heard about his and his saving love through Christ.
The vast majority of mankind, both living and dead, will never ever even hear the name of Jesus Christ, much less know what it is to exercise faith in Him.
The vast majority will never hear of Jesus?
What evidence do you have for that; considering the number of languages the Bible has now been translated into, considering missions work overseas, considering the many, many resources - films, music or Christian books that are now available?
And if someone has no idea what it means to exercise faith in Jesus, why do you believe God will condemn them for something they do not know?
He might have something to say to US - we who have been told to go into the world to preach the Good News. We who have been told to pray for everyone, including our enemies. But how could someone be at fault if the Good News had never reached them?
As you yourself say, God can heal.
Can and does - either through direct, miraculous intervention, or through doctors and medicine. This latter method is still healing.
As we all know, Christians do get sick and eventually die, but God does not miraculously heal all Christians all of the time. He is able to do so, but does not do so.
But that doesn't mean that he can't, or won't, heal at all.
Some Christians seem to have a limited definition of healing - they regard it only as miraculous intervention by God. I've seen it on these very forums over the years; healing through doctors and medicine is sometimes dismissed as "natural recovery", "not really healing" or "it doesn't count." Yet God has given people the ability to discover, and create, medicines, train as medics and so on.
There are many, many testimonies of Christians being miraculously healed - and many more of God answering prayer, guiding, comforting.
So I don't know where you get your idea about God "not entangling himself in the results of sin."