I agree - "God is Love" (1 John 4:8, 16) teaches that God, in His very essence is love. All He does and all His interactions with people are dominated and controlled by love, despite our limited human perspective to the contrary at times.
Jesus made this explicit even for the law in the OP's quotation of Matt 22:37-40.
Too many have erred when they view the Torah as a series of regulation and exactitude controlled by legalism. They appear to forget that when Jesus annunciated the principle of love in the law, He was quoting the Torah itself in Lev 19:18 and Deut 6:5.
Further, Jesus wants His disciples to be similarly motivated and follow the example of Jesus:
- John 13:34, 35 - A new commandment I give you: Love one another. As I have loved you, so you also must love one another. By this everyone will know that you are My disciples, if you love one another.”
- John 15:12 - This is My commandment, that you love one another as I have loved you.
- 1 John 4:8, 11, 19 - Whoever does not love does not know God, because God is love ... Beloved, if God so loved us, we also ought to love one another ... We love because He first loved us.
- Eph 5:1, 2 - Be imitators of God, therefore, as beloved children, and walk in love, just as Christ loved us and gave Himself up for us as a fragrant sacrificial offering to God.
APPENDIX - Love
The Bible does not discuss just one type of love but clearly recognizes several kinds. The Greek language had six words for various kinds of love, but only three of these broad categories are discussed here. They are arranged into a kind of hierarchy – the widest first and the narrowest last.
“Agape” love (Greek: agapao (v) or agape (n))
This is the most general kind of love and does not necessarily involve any sentimentality, feelings nor whim. Nor does this kind of love necessarily involve liking somebody. It springs purely from principle and is often opposed to the natural inclinations. This dependable, abiding and constant love is celebrated in 1 Cor 13. It is others-focused so excludes all self-centredness.
The best definition of agape love is, “God so loved … that He gave His son …” (John 3:16). The “agape” love is the central most important characteristic, the very essence, of God (1 John 4:8, 16). Love’s outward manifestation is grace. It is God as love that defines God and all else about Him such as justice/righteousness tempered with kindness.
This principled love of God (1 John 4:8, 16) is to be imitated by all Christians (John 13:34, 35) and is motivated by God’s love for us (1 John 4:9, 10, 19-21, 2 Cor 5:14). Thus, love is quintessentially Christian and reached its zenith when God gave Jesus as the solution to the sin problem (2 Cor 5:14, Eph 2:4, 3:19, 5:2, John 3:16). Therefore, Christians should have as their primary focus their love of, and love to God (Matt 22:37, Deut 6:5), and secondarily love to fellow humans (Matt 22:39, Lev 19:18).
This word is used to describe God’s love to Jesus (John 17:26) and humankind generally (John 3:16, Rom 5:8). It also describes the love that Christians should have to all people (1 Thess 3:12, 1 Cor 16:14, 2 Peter 1:7).
From this agape love springs all else and expresses itself in obedience to God’s commandments (John 14:15, 21, 23, 15:10, 1 John 2:5, 5:3, 2 John 6). Love is the root of respect for others’ opinions and choices; thus it is also the basis for freedom of choice (which see) and freedom of religion (tolerance of other views).
Isa 63:9 expresses the kind of empathetic love that God has for each person.
“In all their distress he too was distressed, and the angel of his
presence saved them. In his love and mercy he redeemed them; he lifted
them up and carried them all the days of old.”