Paul had the right to be supported by his churches, but he voluntarily set aside that right so that he would not be a burden on them (1 Thess 2:5-10, 1 Cor 9:10-11, 2 Cor 11:7-15, 12:13-18). His refusal to accept gifts from these churches may be related to the poverty of the church (in Thessalonica), or because he did not want to be considered a client of the patronage of the church (Corinth).
But in the Galatian congregations, there were individuals who devoted themselves to teaching and evangelism. For Paul, those individuals ought to cared for by the churches they served. I suspect that this has a parallel in the support of students of the Torah in Judaism, but I cannot lay my hand on a text which could date this early which supports this.
If a local teacher demanded compensation, then I suspect Paul might recommend that they bear their own burden and work for their living. Paul seems to indicate in 1 Thess 2 that the minister of the gospel ought not be a burden, and in 1 Thess 3 that individuals ought to carry their part of the financial load of the ministry. I am fairly confident Paul would have a few acerbic words to say to modern televangelists. Anyone going into ministry in a modern context with the intention of becoming wealthy really ought to find another calling!
Remember, there is no “professional pastor” in the first century. People in a Greco-Roman culture might have devoted themselves to academics (philosophers), relying on patronage to supply their needs. If they were good at what they did, it was possible they received patronage from the wealthy and lived pretty well. Josephus, for example, received the patronage of the Emperor himself when he wrote his history of the Jews and the Jewish War. As an official historian of Vespasian’s major war, he likely was kept well! I expect that the Greco-Roman readers of this letter would have look upon their “pastors” as clients of the patronage of the church. Perhaps this is the problem in Corinth, since there were often strings attached to patronage.