God is not known to be efficient, but He gets the job done by eventually bringing all whom He has chosen to His sheepfold before the night comes.
Several theological principles:
Adam caused the Fall and through Adam and a line of sinful people that the world will be saved. Note how in the genealogy of Jesus (Matt 1:1-17) we have Jacob the liar, Tamar who slept with her father in law (Judah), Rahab the prostitute, and Bathsheba (whom God chose out of David's other wives, even though David murdered her first husband Uriah!)
It's a Biblical pattern that God chose people with problems BUT who have hearts for Him. He dignifies them to be involved in His plan. He is acting like a leader in a company who wants to include everyone in the company's success.
He even helps them to overcome their weakness (like Moses and his speech issue, and Gideon with his fear). He is acting like a father who loves to involve his little children who offer to help their dad to build / repair something although he would have finished the job sooner by himself.
In Christian teaching, a person cannot come to faith unless God first choose him/her (doctrine of election) and then provides him/her with grace to respond to the gospel. Those two are essential, but miracles and vision are not. At the end of the day, despite our evangelizing efforts and powers of persuasion, it is still up to God and up to the person we are evangelizing to.
Conclusion
The reason why God works through His Church is that He wants us (the problem) to be part of the solution. God is control but wants us to be maximally involved. In doing so we become more aware of our sins but become better as a result of evangelizing. His providence and foreknowledge make it work in the end. We look forward to becoming amazed at the extent of God's wisdom when everything is revealed at the end of time.
Paul is our model as his own life becomes the gospel: he started by being a murderer of God's elects, repented, and voluntarily became soldier for Christ suffering for Him out of his gratitude for being saved, and wanted everyone to have the same experience. For more on this theological explanation, I refer you to the 2015 book by NT scholar Michael J. Gorman : Becoming the Gospel: Paul, Participation, and Mission.