I read most of that, and did not weep, 20 years ago when I was getting my degree in aero/astro engineering. Neither of your links support what you're trying to say.

The walls get linearly thicker, and your intuition about why the walls need to get thicker is incorrect.

It's not quite linear. Pressure vessels like air tanks or rocket engines wall thickness scale approximately linearly with radius. But, that's not the only stress on rocket engines which need to deal with thermal expansion etc.

The walls need to get thicker indeed, and that extra thickness gradually adds to the weight of the engine faster than adding extra small engines for the same thrust = less and less payload