>I know proteins are important as structural elements, my question (as ever) is just why?

A couple things. First, a lot of "why" questions in biology are unanswerable, and the explanation you get will come down to quirks of life's evolutionary history.

Second, if I may, I'd like to reframe your question as "Why do we see proteins playing structural roles in the places that we do?" Proteins are just one type of structural molecule, and nature uses many.

Arguably lipids are the most critical structural component for all life since they can form membranes. Cellulose and chitin are polysaccharides (i.e. many sugars linked together) that have structural functions in plants and fungi/arthropods respectively. Lignin is another plant cell wall component, but it is actually a polyphenol. Some organisms even use inorganic compounds to provide structure - bones are obvious, but for a microscopic example look at the silica frustules of diatoms. Even in these examples, it gets messy. You can have several different types of molecules that together form some structural component.

You can think of evolution as a process of blindly stumbling into "solutions" for "problems". In some cases, evolution reaches different solutions for similar problems. Things like hair and fingernails are made of keratin (a structural protein) while insect exoskeletons are made of chitin (a structural polysaccharide). In other cases like the cytoskeleton, you only see protein being used. That brings me back to my reformulation of your question. You can make hypotheses about why this is the case, but they are very hard to test.