Institutes 2.11.3 is exactly what Kline is talking about with his term Intrusion.:
This is why we read that the saints under the Old Testament esteemed mortal life and its blessings more than we ought today. Even though they well knew they were not to stop there as at the end of their race, yet because they recognized what the Lord had imprinted on them to be marks of divine grace to train them according to the measure of their weakness, they were attracted by its sweetness more than if they had contemplated his grace directly. But as the Lord, in testifying his benevolence toward believers by present good things, then foreshadowed spiritual happiness by such types and symbols, so on the other hand he gave, in physical punishments, proofs of his coming judgment against the wicked. Thus, as God’s benefits were more conspicuous in earthly things, so also were his punishments. The ignorant, not considering this analogy and congruity, to call it that, between punishments and rewards, wonder at such great changeableness in God. He, who once was prompt to mete out stern and terrifying punishments for every human transgression, now seems to have laid aside his former wrathful mood and punishes much more gently and rarely. Why, on that account they even go so far as to imagine different Gods for the Old and New Testaments, like the Manichees! But we shall readily dispose of these misgivings if we turn our attention to this dispensation of God which I have noted. He willed that, for the time during which he gave his covenant to the people of Israel in a veiled form, the grace of future and eternal happiness be signified and figured under earthly benefits, the gravity of spiritual death under physical punishments.
“More” than what? More in Israel than in non-theocratic common eras before and since (2.10.23): “Christ the Lord promises to his followers today no other ‘Kingdom of Heaven’ than that in which they may ‘sit at table with Abraham, Isaac, and Jacob’ [Matt. 8:11].”
And what was the lesson God wanted us to learn from Israel? How to build an earthly nation that God would prosper? On the contrary (2.10.20):
I shall warn my readers beforehand to remember to open up their way with the key that I previously put into their hands. That is, whenever the prophets recount the believing people’s blessedness, hardly the least trace of which is discerned in the present life, let them take refuge in this distinction: the better to commend God’s goodness, the prophets represented it for the people under the lineaments, so to speak, of temporal benefits. But they painted a portrait such as to lift up the minds of the people above the earth, above the elements of this world [cf. Gal. 4:3] and the perishing age, and that would of necessity arouse them to ponder the happiness of the spiritual life to come.