It seems like a good idea to me. or add the additional features to Javascript itself?
jQuery exists just because they (browser makers) couldn't agree on common standard.
There's also the issue of versioning. Certain sites and extensions of jQuery require a certain version of jQuery. Right now it's up to the application to decide which version to use.
You can consider jQuery to be a JavaScript plug-in. And browsers do not ship with plug-ins, otherwise the purpose of plug-ins would be irrelevant.
Probably because browsers are hard to update. Some freature of JQuery may eventually make their way into javascript, and I believe some of it has just recently. (well the idea's anyways) It takes years to add a feature to something like javascript, where the JQuery library can just release a new version.
There is actually a firebug or firefox plug in that allows you to inject JQuery into the page.. but thats just a development tool
Because it's just one library of many. It may be popular but it's far from being the only choice. And it would also cause it to freeze at a particular version and make improvements much slower.
Plus there is little advantage anyway. It's fairly small and you can set it to be cachable indefinably by the brower so it will only be downloaded once anyway - if you have a new version it will have a new filename, so there is no harm in making it never expire.
Plugins get updated more often than browsers - within a week the browser version of jQuery would be out of date :)