You write: “For corporate profits to grow faster than GDP (and faster than national income) some other sectors have to lose out.”
It is one of the oldest errors in economics that wages and profits are antagonistic: “And thus we arrive at Mr. Ricardo’s principle, that profits depend upon wages; rising as wages fall, and falling as wages rise.” (Mill, 1874, IV.12)
This relationship holds for a single firm but not for the economy as a whole.* The correct profit equation for the closed investment economy reads Qm=Yd+I-Sm (2014, p. 8, eq. (18)). Legend: Qm monetary profit, Yd distributed profit, I investment expenditures, Sm monetary saving.
When the profit theory is false, then the rest of economic theory is false. The reason why the profit development appears “ominous” to you is that you simply do not know what profit is. That’s rather bad for an economist, isn’t it?
Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
Mill, J. S. (1874). Essays on Some Unsettled Questions of Political Economy. On Profits, and Interest. Library of Economics and Liberty. URL
* For details see ‘As goes GM, so goes America — A rather ordinary fallacy of composition’
Related 'The Profit Theory is False Since Adam Smith. What About the True Distribution Theory?' and 'Essentials of Constructive Heterodoxy: Profit' and 'Proﬁt for Marxists' and 'Debunking Squared'.
It seems that you cannot read. The slice-of-a-pie metaphor is inappropriate for the description of the relationship between wages and profits since Ricardo. Your concept of profit is still on the flat-earth level.
For the derivation of the formally correct Profit Law see ‘How the intelligent non-economist can refute every economist hands down’