My experience is more on the content side than the product side, but we have mostly just abandoned search as a feature. 99.9% of searchers just to go to google. Our on-site search gets nearly zero traction. That's partly self-fulfilling because we've deemphasized it as it dropped in use and is not buried behind nav. But still, I'd generally recommend you invest in SEO and just ignore search.
Yeah, I mean ideally you’re nav is so simple that you don’t need search beyond Google. But it’s not always possible. Take an ecommerce store where the user wants to drill down on particular facets. That needs search (and filter).
No one uses our nav either. Like I said, we produce content so we have >100,000 articles. Our nav lets your drill by broad topics, but really it's just window dressing. It's almost all google, social and direct traffic just looking for whatever is latest. You have to think about what use case search is solving. Usually, it's discovery. People discover through google first and foremost, social and peers secondary. Unless you're Amazon, nobody is using you as a primary source to discover facets of anything.
