The catalyst acid is added only in small amount which is used up only in first step and now H on the N with the positive charge is again very acidic and is strongly picked up by lone pairs of the O of the OH group
I agree with the pKa differential just noted. I'm referring to a different aspect, the O-H-N angle. I suggest we might gain some insight from hydrogen bonds or other proton transfer reactions. In water, the O-H-O bond angle is ~180
o. In an acetate elimination or beta-keto acid decarboxylation, the bond angle is ~120
o. In a Cope elimination, the C-H-O bond angle is ~108
o.
The difficulty I see is that if the electron pairs take up a lot of space, then as that bond angle becomes more and more acute, the electrons would overlap. I perceive this as a much higher energy state, hence my interest in finding an example proving it occurs this way. With protic solvents, one can simply write intermolecular proton transfers (presumably with ~180
o angles). The downside is that one must write an additional steps in the mechanism.