It sounds like there are scenarios where you might want to replace the search with a more specific alternative. For me that suggests that issuing the search functionality as a plugin would be a good idea because it gives the option to replace it outright.

For example a wordpress blog using a membership plugin,is unlikely to be easily searched using Google for premium content (unless they use a first click free system) in such cases they might have to rely on Wordpress own search system, which like everything else is pretty expandable and can be modified with plugins and templates.

c) I just finished writing a simple plugin for a client using our Your Members plugin to allow them to show the “premium” content at the top of search results something she could do with Wordpress but would be difficult to do with a custom search.

d) The information you can get through plugins like search meter not only helps you identify rough numbers of searchers (I suspect its a lot higher then you think) but also what they are searching for, which provides you with the ability to perhaps create hub pages to meet there needs or maybe provide ideas for an articles.

that said Wordpress search sucks there is plenty you could do though Joost did a good Improving Wordpress Search Article not so long ago.

Nathan, I agree that removing it without providing it as an option would be bad. I am a very big fan of using plugins to give options instead of building things into the core, and more so, of removing things from the core that can be made into plugins.

The search functionality is something that could quite easily be a core plugin, as Akismet is, and sit beside other options such as a Google, Yahoo, or other plugin, option.

Leland, that's a good point about a site not indexing well. Still if it was a plugin the choice would be there.

Honestly, I would much prefer to use a google custom search for my blog, and make a little money off my searches, rather than use the inferior and non-monetized built-in WordPress search function.