Sinner's Prayer/Altar Call; Is it Biblical?

I have been thinking a lot lately about the practice of 'sinner's prayer' and 'altar call'.
I have read some history,  and found out that it was a practice developed in the church to facilitate people becoming born again.
I have also been seeing in scripture that it was never so.
When Jesus met the Samaritan woman, she believed in Him. Simply. She believed who Christ told her He is. Simply. No songs, sinner's prayer, nor an alter call. She called people from her village,  and they believed in Christ too. Simply. No sinner's prayer.
The villagers begged Jesus to stay with them, and He did for 2 days. Even more believed in Him. Simply. No alter call, no sinner's prayer.
(Read John chapter 4)
When Jesus taught the thousands of people, He did no altar call. He didn't play music and asked who all wanted to believe in Him to come forward or repeat a sinner's prayer. He taught them. Simply. The people choose to believe in Him. They choose to receive His words.
Whenever I think of a person giving their lives to Christ, automatically I think of sinner's prayer. That I will have to lead them in it, or check if they prayed it. That prayer has become the way to verify that a person is truely born again. Again, from scripture, it was not so.
In Acts, when Peter gave his first sermon, this was the response,  and his response:
Act 2:37& 38& 41 'Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?”
Peter said to them, “Repent, and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of sins, and you will receive the gift of the Holy Spirit.
Then those who gladly received his word were baptized. There were added that day about three thousand souls.
The receiving of God's word, and the believing in God's word is the door to being born again.
We hear God's word, we are convicted, we confess sins and repent of them, and we believe in and receive Christ.
Joh 1:12, 'But as many as received him, to them he gave the right to become God’s children, to those who believe in his name:'
Do we truely believe this? This is God's word. Are we going to hold on to religious traditions and practices, or are we going to believe God's word and obey and follow Him.
(To be continued. ....)