Why default comment fields don’t show up?

Without code and based upon what you are doing, my advise would be to set WP_DEBUG to true in your wp-config.php. If there are any errors causing the fields not to display, they are likely to show up. Especially since you are coding a custom theme, there is a good chance of errors somewhere you wouldn’t expect. If you encounter errors, post them here so we have a little bit more info about what’s going on.