It's not mechanical; it's spiritual.
You must see God's love for us being alien and detached. Perhaps, you would say that God's love for us is like we say we "love a good book"? That is impersonal too. Do you see the word "agape" as being impersonal? If not, then I would ask why you believe that God has personal love for us, but refuses to ever show it
The word agape was used by Christians in a different way as understood by Greek pagan philosophers. Just as the word "gay" used to mean something different 50 years ago as opposed to the present usage (not that the term is in any way related to agape!).
In the Christian context, agape is not intimate love between you and your family; it is a self-sacrificing love of God for humanity. It's pretty impersonal. It's given to us all, but it is not intended for any one of us individually; therefore it is not intimate.
Speaking of John, the disciple Jesus loved, the Bible uses the word "agape," John 13:23, 19:26, etc. as well as the word "philia," i.e. John 20:2 (both of which are translated as "love")
The word agape is found all over the NT, but it is used both as the perosnal love between Jesus and the Father and as a spiritual manifestation for our love for others, indeed the whole world, imperosnally.
Thus in Mat 24:12 (written c. 70 AD) it is used impersonally. Yet, John (whose Gospel is written c. 90-100 AD) uses it as personal love in several places. Paul, on the other hand takes a lot less personal/intimate approach with agape (but remember he wrote between 50-60 AD), such as 1 Cor 13:10, 2 Cor 2:4; he almost defines it in Gal 5:22; in 1 Tim 1:5 and 2:15 it is used as charity, also in Titus 2:2; in Heb 6:10, it is again used in an impersonal manner, 1 Pet 4:8, and 5:14 use agape as charity; also in 2 Pet 1:7; 1 John 2:5 associates it with faith; in 1 John 2:15 it refers to the "love of the world." (doesn't get much more impersonal than that!); but it also associates it with the "love of God;" and in 3 John 1:6 it is used as charity.
The hesycastic fathers postulated, however, that God's love, which exists between the Father and the Son, is not agape, but ἔρως (eros)! The Church teaches that the Holy Spirit is that eros or love between the Father and the Son. Of course, we understand that the word is used to reflect the intensity and not the sexuality of that term.
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Our intellect, because created in God's image, possesses likewise the image of this sublime Eros or intense longing - an image expressed in the love experienced by the intellect for the spiritual knowledge that originates from it and continually abides in it." St. Gregory Palamas ["Topics of Natural and Theological Science" no. 36, The Philokalia Vol. 4 edited by Palmer, Sherrard and Ware; Faber and Faber pgs. 361-362)
I did some more digging and it looks like you're right. "Philia", or brotherly love, is the word that helps me, not so much "agape".
Let me try it this way, if you do not see personal love from God, do you see it in your Church? Does your Church give you something that is greater than what God gives you?
Or, if God does not love us personally then how do you explain this:
Gal 5:22-23 : 22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness and self-control. Against such things there is no law.
If you would agree that all of these are personal, then how can God give us something He doesn't have?