E.g, I have to use a Java app on the Mac that uses Ctrl+V rather than Cmd+V for paste as well as other Windows/Linux keyboard conventions. This is extremely jarring.
Web apps never do that. Browsers are pretty good at using native conventions where it matters by default. Of course web devs sometimes go out of their way to vandalise the browser's perfectly good defaults - e.g. by overriding scrolling behaviour.
Surprisingly, some of Apple's own native apps (such as Numbers) break platform conventions in ways that makes the app extremely inconvenient to use.
In an alternate universe, where web apps were embraced by the platform from the start rather than something people had to shoehorn into a document sharing mechanism, and we had rich components built-in, then yes I would probably be annoyed if people insisted on rolling their own versions. After all, I am annoyed when people use a span with a click handler instead of a proper anchor tag, because it usually breaks middle clicking or opening a link in a new tab—a platform convention I have internalised and expect to work.
Note this only applies to web apps, not sites. Much like how I do not have any problem that magazines don’t share a common layout.
I used to share your opinion but since the web I think it is great that designers can have original designs and I started to worry about more important things.