Photoshop / Illustrator / InDesign - placed image different dimensions and resolution

The same problem over and over again - why do images placed in Id/Ai show different size than in PS?

I've made image in PS of about 2000x1500 pixels at 300 PPI.

Then made Ai document of 2500x1600 pixels at 300 PPI. To avoid any conversion/compression surprises I simply placed the Ps document in Ai document. Guess what? It's shrunk and terribly pixelated though MB size in link properties seems correct. Ok, then maybe for some reason it reduced the resolution: let's make an Ai doc at 72 PPI. Surprise again - the placed PS doc is exactly the same size as it was in 300 PPI doc. And exactly the same pixelated.

Let's try Id then: one with print intent (so it should have like 300 PPI) and one with web intent (should have about 72 PPI), both size like before. Guess what? Absolutely no change - Ps doc is shrunk and pixelated (and appears same size in both cases), though shows correct MB size, Actual PPI = Effective PPI = 300 and correct dimensions according to link description.

When tried with *.png file instead of Ps, nothing changed as well.

I'm totally dumbstruck by now. How is it that suddenly one 300 PPI file is not working with other 300 PPI file and 2000pix height becomes less than 1/5 of 2500pix height?...