Actually, it is what Scripture says it is.
And what we find in Scripture is that administrator and mediator are two different operations in the Trinity.
The Son accomplished the work, and the Holy Spirit is the power of God at work applying its benefits.
As mediator, Christ interposed between God and the elect, effecting reconciliation by his atoning sacrifice,
which purchased the benefits of the New Covenant with his blood.
As surety and guarantee of the New Covenant, Christ guarantees
that we will keep our part of the covenant (faith), and
that God will keep his part of the covenant (salvation).
The Holy Spirit then applies (administers) the benefits of the covenant to God's elect--new birth, faith, conviction of sin, repentance, forgiveness, justification, illumination, witnessing/testifying, sanctification, transformation, preservation in faith, glorification.
We don't have a 'part' to 'keep' in the New Covenant. We enter in by faith, just as Abraham did.
The New Covenant is made within the Trinity; initiated by the Father, ratified with the Blood of the Son, Who administers/mediates/officiates, from a position of rest because His Work is finished
[don't even start with me on that one again, as you continue to make a mountain out of a molehill] by the Son, and sealed by the Holy Spirit:
Jeremiah 31:33-34
33 "For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people. 34 And no longer shall each one teach his neighbor and each his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest, declares the Lord. For I will forgive their iniquity, and I will remember their sin no more.”
Luke 22:20
20 In the same way, after the supper he took the cup, saying, “This cup is the new covenant in my blood, which is poured out for you.
Ephesians 1:13-14
13 And you also were included in Christ when you heard the message of truth, the gospel of your salvation. When you believed, you were marked in him with a seal, the promised Holy Spirit, 14 who is a deposit guaranteeing our inheritance until the redemption of those who are God’s possession—to the praise of his glory.
And the elect are all who receive Christ; it is not that only the 'elect' will receive Christ.
And the Holy Spirit does not convict
believers of sin. There is NO contextual Scripture to support that notion.
John 16:8-11
8 And when he [the Holy Spirit] comes, he will convict the world concerning sin and righteousness and judgment:
9 concerning sin, because they do not believe in me; [That's the unbelieving world.]
10 concerning righteousness, because I go to the Father, and you will see me no longer; [That's those who believe; the Holy Spirit actually convicts us of our righteousness in Christ! He always builds us up in who we are in Christ! \o/]
11 concerning judgment, because the ruler of this world is judged. [That's Satan, who is judged by Christ Col. 2:15.]
The rest of your list feeds right into the Law-keeping crowd's arguments.
In Christ, we ARE the Righteousness of God. There is no improvement on that position.
Regarding our condition in this life, while still in the flesh . . .
Titus 2:11-14
11 For the grace of God has appearedthat offers salvation to all people. 12 It [Grace] teaches us to say “No” to ungodliness and worldly passions, and to live self-controlled, upright and godly lives in this present age,13 while we wait for the blessed hope—the appearing of the glory of our great God and Savior, Jesus Christ, 14 who gave himself for us to redeem us from all wickedness and to purify for himself a people that are his very own, eager to do what is good.
It's really not as complicated as you make it out to be.
If you're in Christ, surrendering to His Life in you, the command to love is not a 'work'; it is not something to 'be obeyed'; the command to love is FRUIT which the Spirit
produces and we
bear:
Galatians 5:22-23
22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such things there is no law.
-JGIG