You sound like Gordon Clark and the Sandemanians, both of which are Calvinists, by the way. The gospel is a set of propositions, but intellectual assent to the set of propositions does not do justice as an explanation of saving faith. One reason is that if you are human belief in something will have an effect on you in accordance with your perception of what it truly means. The bare naked facts of the gospel because of what the gospel means will be received differently as truth than knowledge of a set of new facts of indifferent importance. Just like you would react differently to belief that you won a dozen donuts as compared to winning 50 million dollars. True, the intellectual exercise is the same as far as your brain is concerned, but you should doubt yourself as to whether you really believed it if the reaction was the same.
Another reason "Why does one believe anything" doesn't work for the gospel is that belief in the gospel requires a prior work on our souls or else we will not see the importance of the propositions. This is not the case with believing other things. In believing other things either the knowledge is indifferent to us or we have a natural ability to understand our need to take the thing proposed seriously. If I am a refugee and they tell me I can find food at a certain location that knowledge is important to me and good news because of my natural ability to be hungry and my understanding that I need food. When people hear the gospel their natural state is to think the proposals are foolish or that they are doing OK on their own, already. In a sense, you are technically right in that if they would believe they could be saved, but they see no reason to worry themselves with doing so.
So what you saying is the Gordon Clark and the Sandemanians actually believed the bible So even a calvinist can learn to trust scripture.
It seems you still have a problem trusting scripture when it says
Rom 10:9 that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved;
Rom 10:10 for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation.
So what your saying is that the gospel message is useless. Why did Christ have to suffer in the first place. All God has to do is zap the person and they would believe in Him. On the other hand if He did not zap them then it would be impossible for them to believe so now we have God choosing who will spend eternity in hell even though the bible says we are responsible for rejecting Him.
Joh 20:30 Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book;
Joh 20:31 but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.
What does the bible tell us.
Rom 1:16 For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes,
Eph 1:13 In Him, you also, after listening to the message of truth, the gospel of your salvation—having also believed, you were sealed in Him with the Holy Spirit of promise,
which confirms
Rom 10:13 for "WHOEVER WILL CALL ON THE NAME OF THE LORD WILL BE SAVED."
So it seems you would rather fall to the negative view of the Love of God for His creation in that He only loves some such as A. Pink suggested.