I am not sure if his Dispensationalism plays a part in his interpretation but I will have to respectfully disagree with this take. This was confirmed to me also when I checked some of the older commentaries that saw it differently as well. Jesus is teaching us what those in the coming kingdom will look like. Overall he makes the point that under the New Covenant we will have new hearts that will be driven by love and not merely obeying the rules. This is why in vs. 20 he said, "For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven." The Pharisees, like Israel in the OT at best could render some measure of outward obedience but their hearts were "far" from the Lord. The only obedience that honors the Lord is that done out of love. Later Jesus would explain to Nicodemus that when one enters the kingdom the Holy Spirit gives him a new heart and makes him a new creature in regeneration or the new birth.
Jesus in Matthew 5-7 is not setting up some standard that no one can attain to so that we will realize that we need Jesus's righteousness but instead he is explaining how we serve the Lord under the New Covenant Era. I agree that at some point every Christian has come to realize that we are ruined sinners with no hope of getting right with God without Christ but this isn't what Jesus is driving home in this Sermon. If he was then he would leave the crowd in despair without telling them how to fix the problem. It wouldn't be until some years later after the cross that they would be able to realize how they can be made perfect in Christ.
It seems MacArthur's interpretation has Jesus speaking vs. 48 tongue in cheek; "here is the righteousness the Father demands and by the way you don't have it." But we notice that the cross and the concept of the atonement is not dealt with in this sermon. This interpretation doesn't seem to fit into the context of the sermon. Instead, I would see Jesus answering vs. 20 quoted above. True holiness is not outward conformity to the Law or hypocritical alms giving, etc. but serving the Lord and others out of love. Jesus is saying that if this doesn't describe you but instead your religion looks like the Pharisees then you have a problem.
Everything the Godhead does is ultimately to honor itself and Jesus did all things to please the Father because he loved the Father. Therefore the perfection or the perfect way of holiness is to love God supremely and do everything to glorify him just as Jesus did as an example for us to follow. Jesus is explaining the nature of true holiness and so he says that the holiness that pleases the Father is going to look like the Father. Mature godly living serves out of love it doesn't mindlessly or hypocritically do good works to be seen of men or earn God's grace.
Jesus is telling us to be perfect so it must be something we can do. He isn't talking about being sinlessly perfect but exhorting us to follow the pattern that Jesus laid down for us which he teases out in the Sermon on the Mount. This is mature Christian living, loving even as we have been loved and supports Jesus' later teaching that loving God with all our heart and our neighbor as our self is the sum total of the law of God.