God wants them to rely on the free-will gifts of God's people for their sustenance (1 Corinthians 9:4-14). This is not the same as a person agreeing to pastor a church in return for a salary. If you are an elder/pastor or a missionary/evangelist, and you believe God wants you to be in "full time ministry", that is, leave your job and devote all your time to ministry, then by all means do so. If God has called you to be in full time ministry, you are His employee and He will pay you - through His people. Do not seek employment with a church! Peter never agreed to work as pastor of the Jerusalem church or Babylon church for a certain salary. But God provided for Peter - using His people, of course.
There is a fundamental difference between working for people and being on their payroll (like a secular worker does) versus working for God and being on His payroll, with people merely being the means that God uses to pay you. The first position is wrong and the second is right. Paul was not on the Philippian payroll, but the Philippians did send him a gift (Philippians 4:18).
Those of us who have secular income need to be sensitive to the needs of evangelists and pastors who are doing full time service just as in ancient times, the people of Israel were to be sensitive to the needs of Levites (Deuteronomy 14:27).