From a Christian perspective, all three are essential. Isaiah says there's no limit to God's understanding; Job says He sees everything under the Heavens. John speaks to God literally being love. Jesus says "For all things are possible with God" in Mark. Aquinas argues for their inter-necessity in the
Summa Theologica. Any Christian God is undoubtedly all three. I can't speak for other religions, though.
God could be all-loving in the true/objective sense, God is all-loving from his point of view, but it might not line up with what some individuals would consider all-loving from their point of view (or maybe they would, if they had God's knowledge).
This is almost certainly true, and I don't see why it would be an argument against all-loving in anyway.
