Dear Anton:

Thank you for the question.

It might seem to be a contradiction, but there is none. There is a difference between Baptism of Desire and the Sacrament of Baptism that explains this appearance of contradiction.

St. Thomas Aquinas explains (bold is my emphasis):

As stated above (1, ad 2; 68, 2) man receives the forgiveness of sins before Baptism in so far as he has Baptism of desire, explicitly or implicitly; and yet when he actually receives Baptism, he receives a fuller remission, as to the remission of the entire punishment. So also before Baptism Cornelius and others like him receive grace and virtues through their faith in Christ and their desire for Baptism, implicit or explicit: but afterwards when baptized, they receive a yet greater fullness of grace and virtues. Hence in Psalm 22:2, “He hath brought me up on the water of refreshment,” a gloss says: “He has brought us up by an increase of virtue and good deeds in Baptism. Yet catechumens who die without baptism can be saved but only as through fire. That is, they are absolved of eternal punishment, not temporal punishment.”
—STh III, q. 69, a. 4.

A further explanation:

No man obtains eternal life unless he be free from all guilt and debt of punishment. Now this plenary absolution is given when a man receives Baptism, or suffers martyrdom: for which reason is it stated that martyrdom “contains all the sacramental virtue of Baptism,” i.e. as to the full deliverance from guilt and punishment. Suppose, therefore, a catechumen to have the desire for Baptism (else he could not be said to die in his good works, which cannot be without “faith that worketh by charity”), such a one, were he to die, would not forthwith come to eternal life, but would suffer punishment for his past sins, “but he himself shall be saved, yet so as by fire” as is stated 1 Corinthians 3:15.
—STh III, 68, a. 2 ad 2 

 The Baptism of Desire includes a perfect act of contrition and a sincere desire to be baptized if that were possible. But, the Baptism of Desire does not contain within it the plenary absolution that is contained in the Sacrament. It is the plenary absolution that "remits temporal punishment due to sins." Thus, a person who dies with perfect contrition and a desire to be baptized, but without the plenary absolution, must undergo "temporal punishment due to sins," a purging of his soul as stated by St. Paul in 1 Corinthians 3:12-15

  12 Now if any one builds on the foundation with gold, silver, precious stones, wood, hay, stubble— 13 each man’s work will become manifest; for the Day will disclose it, because it will be revealed with fire, and the fire will test what sort of work each one has done. 14 If the work which any man has built on the foundation survives, he will receive a reward. 15 If any man’s work is burned up, he will suffer loss, though he himself will be saved, but only as through fire.

Plenary absolution (Plenary Indulgence) removes (remits) this purging and one goes directly to heaven. Otherwise, we go to purgatory first to experience this purging before entering the throne room of God.

Baptism of Desire does not include the Plenary absolution. It also does not include the imprint of the baptismal character. Baptism of Desire, since it is not a Sacrament, does not give access to the other Sacraments, nor to a Plenary absolution, which is granted only to those who have received the Sacrament. As explained by Father John Hardon:

Baptism of desire is not a sacrament; it does not imprint the baptismal character or enable a person to receive the other sacraments. Nevertheless, it does confer sanctifying grace.

As to your second question on why God does not protect a person from death until he receives the Sacrament: The one-liner answer is 1) effects of original sin; and 2) Free will.

1) Effects of Original sin effects us all. Death is one of those effects. Thus, death by natural disaster, non-culpable medical issues, and the like are things that are simply part of life in a fallen world. God does not normally protect is from these natural effects. In some cases he may perform a miracle to protect someone, but that is the exception not the rule. Who God chooses for such miracles is known to God alone.

2) Most of our problems, however, are caused by Free Will. Premature death is often caused by the choices we or others make. Even medical problems may be as result of choices we made about healthy living. Nearly all auto accidents are a result of choices made by us, or by another driver. We oftentimes suffer the consequences of someone else's free will choices.

God will never intrude upon our free will. If he did we would no longer be human being made in His image. Free will is like pregnancy — either you is or you ain't; one cannot be 99% pregnant. One cannot enjoy 99% free will. Free Will must be total (100%) or it is not free.

This is why God, in his infinite mercy, allows one to receive sanctifying grace to those who desire baptism with perfect charity (perfect contrition). The same mercy is shown to the Baptized Christian when he sins and offers a perfect act of contrition but dies before making it to the Sacrament. These people will be with God in heaven forever, but through purgatory first (which is what will happen to most of us anyway). God does not desire anyone to perish. God loves us so much that he provides for these situations where the Sacrament is not possible before death.

I hope this helps.

God Bless,
Bro. Ignatius Mary