I do not know if it always has been the case with the Christian churches that there has been the emphasis on evangelism that is true of today. I do not see this emphasis in the New Testament. The Great Commission seems to stress making disciples, not getting people "saved." Anyway, the Great Commission was addressed to the Apostles of Christ, not to the rank and file of believers.
The same thing is true of "Go into all the world and preach the Gospel to every creature." This was addressed to the "Eleven."
The office of evangelist is only one of numerous gifts and ministries given by the Holy Spirit to the Body of Christ.
The idea that "we are saved to save others" hardly is scriptural.
I have thought about this emphasis on evangelism for many years. How often do pastors and evangelists urge every member of the congregation to "get out and get the lost saved." Perhaps it is because the larger the attendance becomes the more important the church appears in the view of the denomination and the community.
In other words, the number in attendance is an indicator of success or lack of it. The pastor or evangelist who is mentally healthy wants to be a success. So there may be no spiritual growth whatever on the part of the people who attend; but if there is a large attendance, the church is regarded highly and the pastor is considered to be successful.
If the people of the congregation are bound with bitterness, unforgiveness, hatred, gossip, it is unfortunate. But the first priority is to keep growing in numbers.