You are missing the point. The argument was can a person desire to become a Catholic and 'poof' it happens. Baptism of Desire is one example in the affirmative. Can a Protestant desire to be a Catholic and 'poof' it happens? Of course. the conversion is in the desire. If the desire is genuine, the converted Protestant will follow through with formerly becoming a Catholic via the physical sacraments. The point is, that it is possible; that genuine Catholic desire can save a soul who does not get the opportunity to follow through with partaking in the other sacraments.
True Faith is not found outside the Church. No one can obtain true Faith by desiring it super duper hard because you must be united to the Mystical Body Of Christ in order to possess it. No one outside the Church can become a member of the Church by desiring it super duper hard because they lack Divine Faith.
They cannot please God, they cannot have true Faith, they cannot obtain eternal salvation, without being a member of the Church. That is why becoming an actual member of the Church is absolutely necessary for salvation.
You see, dearly beloved sons and venerable brothers, how much vigilance is needed to keep the disease of this terrible evil from infecting and killing your flocks. Do not cease to diligently defend your people against these pernicious errors. Saturate them with the doctrine of Catholic truth more accurately each day. Teach them that just as there is only one God, one Christ, one Holy Spirit, so there is also only one truth which is divinely revealed. There is only one divine faith which is the beginning of salvation for mankind and the basis of all justification, the faith by which the just person lives and without which it is impossible to please God and to come to the community of His children.[2] There is only one true, holy, Catholic church, which is the Apostolic Roman Church. There is only one See founded in Peter by the word of the Lord,[3] outside of which we cannot find either true faith or eternal salvation. He who does not have the Church for a mother cannot have God for a father, and whoever abandons the See of Peter on which the Church is established trusts falsely that he is in the Church.[4] Thus, there can be no greater crime, no more hideous stain than to stand up against Christ, than to divide the Church engendered and purchased by His blood, than to forget evangelical love and to combat with the furor of hostile discord the harmony of the people of God
Pius IX Encyclical Letter 3/17/1856