Why would someone want to copy the native OS UI for a web app? That will just make people think your app is poorly made, when the controls look identical to those from their mobile device's native OS, but function in a hobbled-via-Webkit-limitations manner.
Making something aesthetically ... harmonic ... with the native UI is fine, probably encouraged, but don't set you and your users up for disappointment and frustration by replicating the aesthetics of controls you can't replicate functionally.
Somewhat unrelated to this post, but I'm finding the debate over web vs. native mobile apps to be very interesting.
I'm a huge proponent of web apps for desktop apps. Most software is simple enough to work well in a browser and you can't beat being able to use the same app on any computer without ever installing or upgrading. This advantage seems to disappear on mobile phones though. I carry my phone everywhere I go, so portability isn't really an issue. Most phone platforms provide an easy way to install and keep your apps up-to-date, so that concern fades away too. Most importantly though, I see native mobile apps having a much better user experience than web apps (regardless of whether or not the webapp was written for a mobile platform). On the desktop, I can keep a web app loaded and running all day. That seems a lot harder to do on a phone.
Palm is unveiling their webapp based phone soon. Google says it wants to make more apps using HTML 5. It will be interesting to see how these strategies pan out.
My bible says that you keep as desktop apps those things which you are somehow personally invested in. So for me, that's my to-do list, Mail.app, iTunes, iChat, and Textedit. In other words, the things which I almost constantly use.
Everything else can be put online, though HTML 5 isn't as good at making things look pretty as, say, Cocoa.
As a similar mac user, I would agree. However, when I flip flop to other platforms, the native experience isn't so great - so outside of the mac, I can see the general desire to just make the web the UI for any and all productivity apps at least (and who knows, perhaps even richer apps and 3d stuff in the future).
Its funny, on a mac, if you time things with a watch its not "fast" - loading times, and so on, but the experience is smooth enough that I find the native apps quite nice to quickly open, jot down a note and move on (eg evernote).
That's actually something I noticed on the Mac. It's good at staying sleek enough that on the desktop you notice a difference.
On Windows I used Google Apps for nearly everything. The desktop equivalents weren't good enough to be worth switching to. I'd still take Google Docs over OpenOffice instantly. So my desktop argument only stands when the desktop things are so good that a web equivalent wouldn't work. I doubt I could ever find an online to-do list as good as The Hit List, for instance.
There used to be a web framework in Java (I can't remember the name) which made your web app look like Windows: every box was movable, resizable, they even had pointless minimize and maximize buttons. You couldn't invent a more pointless and annoying UI for the web.
Making something aesthetically ... harmonic ... with the native UI is fine, probably encouraged, but don't set you and your users up for disappointment and frustration by replicating the aesthetics of controls you can't replicate functionally.