How does the essence–energies distinction differ from the ontological/economic views of God?

Eastern Orthodoxy has an emphasis on mystical union with God which goes towards deification through “the Energies”.

Orthodoxy teaches that it is/has the apostolic faith, and although there is agreement with it across the Christian board that all theological knowledge is based upon God’s self-revelation, Orthodoxy includes Apostolic Tradition as a divine source. (A view that Catholicism holds for itself too.) In Orthodoxy, this heritage, or “Deposit of Faith”, is seen as a new reality or new life made available to the world by the incarnation of the Word and through the operation of the Holy Spirit, and the Orthodox hierarchy has, it claims, kept this Deposit of Faith without distortion, just as the apostolic church received it.

Because you asked, "why would many Western theologians consider the essence–energies distinction to be heresy?" I now refer to an article written by a Protestant, because Reformed Protestantism also views this Eastern Orthodox teaching as heretical. This is my summary of several pages:

Protestantism would not agree with this essence-energies distinction, nor with the Catholic emphasis, due to a theological paradigm of creation-fall-redemption, while the Eastern is creation-deification (or theosis). The Protestant Reformation emphasized the legal (forensic) aspect of humanity’s relationship with God. Salvation cannot be earned or merited but is received by faith apart from good works. But Orthodoxy has a mystical approach; God cannot be known intellectually but only experientially, taking “the mystery” of God as reason for saying God is incomprehensible and inconceivable. Orthodoxy says the purpose of theological knowledge and church practice, such as the sacraments, is to help the faithful attain mystical union with God, or deification (theosis). Protestantism would differ on those points.

Source from which the above summary was garnered: Christian Research Journal Vol. 20 No. 3 article by Paul Negrut, pages 26-35.

Another source throws a little light on the query in the question regarding Athanasius, for it shows what he taught regarding aspects of the Trinity relevant to this question. After detailing metaphysical and soteriological points Athanasius made, the author writes:

"In the background of Athanasius's thoughts and arguments here was the traditional idea of salvation as deification (theosis), although his mode of reasoning did not necessarily depend entirely upon it... the solution was deification by means of humanity and divinity being joined in the incarnation. It was Athanasius who provided the most famous expression of this 'wonderful exchange' theory of salvation: 'For he was made man that we might be made God...'

Irenaeus had developed and exploited the concept of salvation as deification (partial participation in God's own immortal energy and life) in order to prove the necessity of Christ's humanity against the Gnostics. Athanasius exploited the idea in order to prove the necessity of Christ's deity against the Arians and semi-Arians... But Athanasius knew that... the ultimate argument had to come back to the reality of the gospel itself. The gospel is about salvation through Jesus Christ, and if Jesus Christ was not God and human, then he could not bring the two together. Salvation would then ultimately be reduced to living a good moral life (Christian moralism) or else gaining some secret knowledge (gnosticism) or merely having one's sins forgiven but being left in the same fallen and corrupt condition as before."

"Gregory frequently used the term theosis (divinization or deification) for the process of salvation and, like Athanasius, considered salvation a process of grace transforming humans into partial participants in the divine nature through 'the wonderful exchange' of the incarnation...

Of course, as explained earlier the idea of salvation as theosis, or divinization, in Eastern Christian thought never means that humans can actually cross the divine-creature divide." The Story of Christian Theology, p169-171 & p189, Roger E. Olson, Apollos 1999.

Conclusions: Because Athanasius's theology left some questions unanswered, so that he was said to have been an Apollinarian before Apollinarius (who was declared heretical at the Council of Constantinople in 381), something of a divide developed, and false gospels began to creep in. It would appear that the Eastern Orthodox emphasis on 'mystical union with God through the Energies' has strayed along this direction. It has brought in a Gnostic element to Christian belief, so that faith is firmly linked to a mystical experience, with no questions asked because the essence of God cannot be known; the Orthodox hierarchy has to be looked to for experience of this mystical union with God.

Time has shown a wandering away from the biblical gospel, and towards mystical gnosticism. That is as simple a conclusion as I can arrive at. It may be far too simple for this question , but researching this question has helped me to grasp a complex issue more easily.