Your assumption that "Jesus will reign only until all enemies have been placed under His feet" is not correct. Jesus's reign is forever, a truth to which the scriptures you cited attest. Here is another scripture that attests to the eternal reign of Jesus Christ:
The seventh angel sounded his trumpet, and there were loud voices in
heaven, which said: “The kingdom of the world has become the kingdom of our Lord and of his Messiah, and he will reign for ever and ever" (Revelation
When (or after) Jesus has "abolished all rule and authority and power" and "put all his enemies under his feet," including death, only then will he hand over the kingdom to God the Father" (1 Corinthians 15:24). Moreover, Paul adds, "the Son himself will be made subject to him who put everything under him, so that God may be all in all" (ibid., v.28, my emphasis).
In other words, there will never come a time when "everything" is not under the Son.
Neither verse 24 nor verse 28 teaches that Christ will be dethroned. His reign is indeed forever. By the same token, however, in his reign, Jesus will be subject to his Father who has put everything under his Son. To be subject to his Father, Jesus is in no way stepping down from his eternal throne, nor is he in any way relinquishing any of his attributes as God the Son, including omnipotence.
The eternal order has been, is now, and forever will be: Father, Son, and Holy Spirit. Within that divine order, there is perfect equality among the three persons of the Trinity. Each person in the Godhead, however, has an eternal role to play. In very human terms, which I use reverently, God the Father has delegated tasks to his well-beloved Son, with whom he is well pleased (see Matthew 3:17; 17:5; Mark 1:11; 9:7; Luke 3:22; 9.35; and 2 Peter 1:17).
In the human sphere, particularly in the workplace, we sometimes assume that the employee is somehow less than, or inferior to, the employer. After all, the employer signs the paychecks, and the "boss" has more power than the people who "report to" her or him. He or she has the authority to dismiss an employee for any reason.
Not so in the divine sphere. The Father is the Sovereign LORD (YHWH). The Son, the Second Person of the Trinity, is subject to the Father and is perfectly obedient to him (see John 8:29). There is a mutual love affair, so to speak, between Father and Son. The Father loves his Son, and the Son loves his Father.
The Holy Spirit's role seems to be to reveal Jesus to all created beings, particularly to true believers in Jesus (see John 14:15 ff.) Jesus called him "the Spirit of truth" (ibid., v.17). So, Jesus IS the truth, and the Spirit of truth reveals him to people. The Holy Spirit who indwells each and every believer in Jesus Christ is Christ's presence with them. He is the Paraclete who teaches them, comforts them, helps them to pray, and empowers them to manifest the Fruit of the Spirit. In so doing, He enables Christians to become more like Christ.
I'll conclude my remarks by providing you with the words of the Isaac Watts hymn, "Jesus Shall Reign":
Jesus shall reign where’er the sun
Does its successive journeys run;
His kingdom stretch from shore to shore,
Till moons shall wax and wane no more.
To Him shall endless prayer be made,
And praises throng to crown His head;
His name like sweet perfume shall rise
With every morning sacrifice.
People and realms of every tongue
Dwell on His love with sweetest song,
And infant voices shall proclaim
Their early blessings on His name.
Blessings abound where’er He reigns:
The pris’ners leap to lose their chains,
The weary find eternal rest,
And all who suffer want are blest.
Let every creature rise and bring
The highest honors to our King,
Angels descend with songs again,
And earth repeat the loud amen.