Only protestants do that. Catholics and orthodox approach the matter a little differently. To be truthful, I don't know what gospel they preach. It used to be the gospel of membership in their church along with being at least being nominally catechized and the sacraments, which does presuppose correct belief in Jesus as savior.
The early Christians were converted through testimony and being pointed to a structured church (although more loosely structured than the monolithic western model we have now), baptism, sacraments, etc., with little drawing on the word because they didn't have a new testament as we know it now. I think, to be fair, they have tended to follow that model throughout history more than relying on the written word alone for purposes of conversion.
Drawing from the scriptures has gained a lot of converts since the invention of the printing press and the education of the masses who can read them for themselves as they were unable to do for centuries. It is fraught with some obvious difficulties as few are in absolute agreement about the scriptures really mean and how they should be correctly interpreted.
Personally, for now, I accept both systems of belief if one is doing the best they know how to follow Jesus and what they understand of his teachings.
As a Calvinist I do believe God's will, will be done no matter what our failings our. God will elect His chosen.
That being said we all have an obligation to share the message of our Lord Jesus Christ and Him crucified. At the risk of sounding hypocritical I find it much easier to write my thoughts than to verbally share them. I fail in knowing the correct things to say and the right time to say it. Generally it comes out, "Accept Jesus Christ today or you're going to Hell." (or something like that). Not exactly effective witnessing. :O)
While I understand the Catholics tend to be slightly different, as you correctly pointed out the catechism contains much scriptural reference. I personally don't think the Vatican want to ruffle any feathers.
For all the opinions and theologies floating around it boils down to confessing with your lips and believing in your heart that Jesus is Lord. While we all sit around debating theology, those who are visiting the widows and orphans will receive the greater reward.