I am not very happy with this "default category requirement" thing.
It is easy to disrupt it but there could be a lot of places where it hides.
But it seems easy enough to get rid of it. I've just set the option in the table to 0 and removed the form elements from /wp-admin/options-writing.php.
I don't think it will bug me any more. It seems to be treated like it is some essential design principle or feature or necessity but that is hardly the case. Posts that get added without category just don't end up in the taxonomy relations table. There might be some code that does a join between the posts and the taxonomy relations, but it doesn't seem like Wordpress' own code is dependent on that. Only my own provisionary code did such a thing.
Feels much better. I modified the "delete category" text too. Only harmony now. I just absolutely love Wordpress because it is such clean code and so very easy to modify. I'm not even backing these files up or keeping a changelog if some minor automatic update replaces a file I'm cool with that.
So thank you all for this great product and this amazing hacks forum and the only thing I am going to remove now is this hypocritical "Thank you for creating with WordPress." line that thinks it is smart enough to have a place on my computer.