Not making excuses, or maybe I am, but:
The main use I see for searching bookmarks is to find that annoyingly absent one I can remember and place more prominently. Since, as you said, the desktop version will search, and both Safari and Chrome will sync with the iOS versions you can do any maintenance and re-arranging there.
Though I do think being able to search for it in real time could be useful, and I'd probably hate losing it if I ever got used to the feature.
But what I actually do when I want an organized set of bookmarks is use Evernote. It's a little more trouble to add and organize bookmarks there, but the payoff is huge. Evernote is available just about anywhere. It has great organizational and search tools; far beyond what you can find in any browser. You can add full descriptions for each link (making it much more searchable). Tapping a link in Evernote takes you neatly to the site you in Safari. And you can actually do something with the links other than just go to the site; like copy and paste them into a forum post, conveniently even.
If you stick around you'll see I often provide the same links and even text to problems; word for word. Evernote is the reason. Well, that and I'm lazy. The third or fourth time I have to look or type something up I tend to take the extra few seconds to note it.
I tend to go on, and on, and… ...about Evernote, but I find it extremely useful for all kinds of things; things you don't normally think of when considering a note application.