This statement is nothing more than your opinion based on the trust only regeneration theology. To accept this theology is to ignore the flow and form of the entire Bible. The labeling of obviously general statements as definitive is central to its acceptance. Your adding of "All-sufficient" to your understanding of 1st Cor. 15:1-4 & Romans 1:16 is a classic example of this mindset.
The word translated believe is found in the Greek lexicon of the Strong's Exhaustive Concordance and is defined as follows: #4100; pisteuō which means "to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to *entrust (especially one’s spiritual well being to Christ).*
The word translated faith is found in the Greek lexicon of the Strong’s Exhaustive Concordance and is defined as follows: #4102; pistis; persuasion, i.e. credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher), *especially reliance upon Christ for salvation;* abstractly, constancy in such profession; by extension, the system of religious (Gospel) truth itself:--assurance, belief, believe, faith, fidelity.
The word "believe" can describe mere "mental assent belief," as in James 2:19, or also include "trust and reliance in Christ for salvation," as in Acts 16:31. In James 2:19, the demons believe "mental assent" that "there is one God" but they do not believe/entrust their spiritual well being to Christ; have faith/reliance upon Christ for salvation.
Yet since you seem to think that ALL belief is the same "except for the lack of works" and cannot grasp a DEEPER faith which trusts exclusively in Christ for salvation you fail to grasp the truth. This also explains why you have so much faith in "water and works."
There is nothing in their wording to assume these verses are defintive. On the contrary, the lack of any words such as alone, only or solely is damning evidence of its general nature. The absence of even the level or nature of belief is more than enough to label them as simply general statements of the essence of Christianity. Any high school English composition student can easily see this.
In other words, your reliance on general statements to defend a "all-sufficient" faith alone theology is far from convincing.
The gospel is the "good news" of the death, burial and resurrection of Christ (1 Corinthians 15:1-4) and is the power of God unto salvation to everyone that BELIEVES.. (Romans 1:16).
2 Corinthians 4:3 But if our gospel be hid, it is hid to them that are lost: 4 In whom the god of this world hath blinded the minds of them which BELIEVE NOT, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them.