Our fifth reason for not doing prayers for healing in evangelism is that it makes someone come to Christ "For the wrong reasons":
When an unbeliever is told by a well-meaning Christian that God always wants to heal, he’ll easily think “Ok I can get on board with this. I’ll become a Christian to get some healing. That’ll be cool. That will make my life a bit easier.” - which is a completely wrong motivation for someone to become a Christian.
Why? For the person will only stick around while he gets what he was promised. Inevitably he will get sick or injured and eventually die of some bodily failure (which everyone dies from), and he'll see that the promise that the well-meaning Christian made didn't come true.
It reminds me of those that were fed in the feeding of the 5000, they wanted to follow Jesus because he could keep giving them free bread. So Jesus tells them, "You're only following me because you ate the bread" (John 6:26) and he instead points them to the eternal need they have. We then read at the end of that chapter, everyone except the Twelve stopped following Jesus. When there was no more expectation of free bread, they gave up.
The Bible doesn't say that God always want to heal a person, instead it says that a Christian will also undergo many hardships and even persecution for following Christ.
So the central motivation someone should have for coming to Christ is to receive forgiveness of sins, not healing. That way when the hardships of following Christ come, the person won’t give up because he hasn’t come to have an easier life now, but he has come because he knows that without being in Christ, he will be under God’s punishment forever.
So let’s not make superficial converts or make false promises, but instead continue pleading with people to come to faith in Christ while God is offering mercy, for punishment is coming. That way they'll be coming for the right reason.