First let me say that I am not at all trying to discount faith; without it baptism would be no more helpful than being dunked in the pool. Nor am I trying to be disrespectful, and if anything sounds that way, I apologize in advance. That being said...
If the conversion of the Philippian jailer were the only example of or teaching on salvation we had, I would agree with you. But it's not so we have to take the whole of the Bible, not just that one thing. There are so many verses that connect baptism with salvation, like the one I already mentioned (which I have never heard anyone give a defense for without basically ignoring it) or 1 Peter 3:21. "There is also an antitype which now saves us—baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ." What about Paul? He prayed for three days in Damascus and if anyone could have been saved by just faith (or prayer, as some say) it would have been him. But still Ananias said to him, "And now why are you waiting? Arise and be baptized and wash away your sins, calling on the name of the Lord." (Acts 22:16)
Yes, people were baptized before Jesus' death, but the reasons were different.
I know the action can become isolated from the faith, but that doesn't mean it should be. And baptism doesn't mean that you can later live selfishly and still go to Heaven.
"What does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him? If a brother or sister is naked and destitute of daily food, and one of you says to them, 'Depart in peace, be warmed and filled,' but you do not give them the things which are needed for the body, what does it profit? Thus also faith by itself, if it does not have works, is dead.
"But someone will say, 'You have faith, and I have works.' Show me your faith without your works, and I will show you my faith by my works. You believe that there is one God. You do well. Even the demons believe—and tremble! But do you want to know, O foolish man, that faith without works is dead? Was not Abraham our father justified by works when he offered Isaac his son on the altar? Do you see that faith was working together with his works, and by works faith was made perfect? And the Scripture was fulfilled which says, 'Abraham believed God, and it was accounted to him for righteousness.' And he was called the friend of God. You see then that a man is justified by works, and not by faith only.
"Likewise, was not Rahab the harlot also justified by works when she received the messengers and sent them out another way?
"For as the body without the spirit is dead, so faith without works is dead also." James 2:14-26 Faith is necessary. Works are equally so.