I agree with what you're saying; however, I'd like to clarify this statement "we are to try and live a life of 'less sin.'"
Paul says emphatically that there are certain acts of sin, if practiced, will prevent a person from inheriting the kingdom of heaven (1 Cor. 6 et al). For example, if I was an adulterer before conversion, and I commit adultery less after conversion, am I still born again? The way I read scripture, "less sin" doesn't cut the mustard here. Less adultery is still practicing adultery, and Paul declares such people will not be entering heaven.
So "less sin" has to be limited to things not in the infamous list, things like trying to treat people better, getting help concerning addictions, etc. Rom. 8:12-14 "brethren, we have an obligation, not to live according to the flesh; because if you live according to the flesh, you shall die; but if by the Spirit you are putting to death the deeds of the flesh you will live, for all who are led by the Spirit of God are the sons of God."
Christians who live carnal lives should justly have a guilty conscience and question their salvation. Only when a person sincerely repents from sin, trusting Christ for deliverance, does a person enter the promise of rest and experience peace with God. For example, if I look down on others, I should be seeking for the Spirit to change my attitude toward others, since Paul calls that "vain glory."
My point is, there are minor sins that people can easily forgive and tolerate, as we should, to be patient for others to become more mature in the faith. Such sins we might tolerate in ourselves, if they can be called sins, because of personality defects. But sins that the Bible explicitly says that God will not tolerate should not be tolerated by us; rather, we ought to take Biblical warnings seriously.
My point in all this is to clarify the term "sins" that is usually kept vague, and make distinctions between sin leading to death and sin not leading to death, as John does in 1 Jn. 5.