Stabilizing forces between the protein sequences?
Proteins often undergo conformational changes. The activation energy required to undergo a conformational change in a protein with only covalent interactions would be much higher compared to that of a protein with weaker bonding forces. An example of a conformational change seen in enzymes is the change in conformation during allosteric regulation, in which an effector molecule binds a site on the enzyme distant from the enzymes active site. The binding of the effector molecule induces a conformational change that exposes the active site of the enzyme. Another example of conformational change is the change in conformation seen in Toll-Like-Receptors (TLRs). Additionally, many proteins change their conformation in response to pH. These changes would likely not occur if the protein only contained covalent bonds, and the ability of proteins to undergo such changes makes them responsive to the environment, as well as allowing them to carry out their enzymatic actions, if such actions exist for that particular protein.

Here is the wiki on allosteric regulation https://en.wikipedia.org/wiki/Allosteric_regulation

Here is a figure on conformational changes in TLRs http://www.nature.com/ni/journal/v8/n7/fig_tab/ni0707-675_F1.html

And here is the wiki on activation energy, a concept used in chemistry (see section on catalysis and Gibbs free energy) https://en.wikipedia.org/wiki/Activation_energy