As a note regarding non-covalent interactions, unfolded proteins still experience non-covalent interactions. However, they are predominantly inter-molecular as opposed to intra-molecular.

Your list defines the difference between the folded and unfolded state of globular proteins. globular proteins in the unfolded state are frequently highly aggregation prone and need high concentrations of agents such as urea or guanidinium hydrochloride to stay in solution

However there are also natively unfolded (intrinsically disordered) proteins or parts of proteins. These frequently have high charge to make them soluble, few hydrophobic residues, but may have biological activities, either assuming a define structure upon complex formation with a partner protein, or even form disordered complexes.

e.g. see

Borgia, A., Borgia, M., Bugge, K., Kissling, V.M., Heidarsson, P.O., Fernandes, C.B., Sottini, A., Soranno, A., Buholzer, K., Nettels, D., Kragelund, B.B., Best, R.B. & Schuler, B. (2018) Extreme disorder in an ultrahigh-affinity protein complex. Nature 555, 61-66. https://schuler.bioc.uzh.ch/wp-content/uploads/2020/04/borgia18schuler.pdf See News & Views by Berlow & Wright (2018): “Tight complexes from disordered proteins” Nature 555, 37-38. https://schuler.bioc.uzh.ch/wp-content/uploads/2020/04/berlow18wright.pdf

Annemarie Honegger What you said is correct. However, the publication you have mentioned about an extremely tight affinity of a disordered complex might not be the best example. The results in that publication have been put into question:

Article The binding affinity and function of the extremely disordere...

I know the paper cited is an extreme example - however, it is one there we have actual experimental data (single molecule FRET) proving that the complex does not transiently assume a folded structure upon assembly.

Yes, I agree about the fuzzy complex, but not sure about the extreme affinity according the Biochemistry paper