Add Post Screen Keep Category structure

Yup.

Use the add_meta_boxes_post to add a new category metabox that preserves the structure and while you’re at it, remove the default one, like this:

add_action( 'add_meta_boxes_post', 'fix_hierarchical_post_categories_metaboxes', 10, 1 );

And here’s the callback:

/*
 * This include provides an alternative post category metabox that sets the checked_ontop argument of wp_terms_checklist to false.
 * This prevents the re-ordering of selected category items to the top of the list, instead preserving their hierarchical
 * order.
 */

function fix_hierarchical_post_categories_metaboxes( $post ){
    global $wp_meta_boxes;
    foreach ( $wp_meta_boxes as &$post_metaboxes ){
        foreach ( $post_metaboxes as &$position_metaboxes ){
            foreach ( $position_metaboxes as &$priority_metaboxes ){
                foreach ( $priority_metaboxes as &$metabox ){
                    if ( $metabox['callback'] == 'post_categories_meta_box' ){
                        $metabox['callback'] = 'hierarchical_post_categories_meta_box';
                    }
                }
            }
        }
    }
}

function hierarchical_post_categories_meta_box( $post, $box ) {
    $defaults = array('taxonomy' => 'category');
    if ( !isset($box['args']) || !is_array($box['args']) )
        $args = array();
    else
        $args = $box['args'];
    extract( wp_parse_args($args, $defaults), EXTR_SKIP );
    $tax = get_taxonomy($taxonomy);

    ?>
    <div id="taxonomy-<?php echo $taxonomy; ?>" class="categorydiv">
        <ul id="<?php echo $taxonomy; ?>-tabs" class="category-tabs">
            <li class="tabs"><a href="#<?php echo $taxonomy; ?>-all" tabindex="3"><?php echo $tax->labels->all_items; ?></a></li>
            <li class="hide-if-no-js"><a href="#<?php echo $taxonomy; ?>-pop" tabindex="3"><?php _e( 'Most Used' ); ?></a></li>
        </ul>

        <div id="<?php echo $taxonomy; ?>-pop" class="tabs-panel" style="display: none;">
            <ul id="<?php echo $taxonomy; ?>checklist-pop" class="categorychecklist form-no-clear" >
                <?php $popular_ids = wp_popular_terms_checklist($taxonomy); ?>
            </ul>
        </div>

        <div id="<?php echo $taxonomy; ?>-all" class="tabs-panel">
            <?php
            $name = ( $taxonomy == 'category' ) ? 'post_category' : 'tax_input[' . $taxonomy . ']';
            echo "<input type="hidden" name="{$name}[]" value="0" />"; // Allows for an empty term set to be sent. 0 is an invalid Term ID and will be ignored by empty() checks.
            ?>
            <ul id="<?php echo $taxonomy; ?>checklist" class="list:<?php echo $taxonomy?> categorychecklist form-no-clear">
                <?php wp_terms_checklist($post->ID, array( 'taxonomy' => $taxonomy, 'popular_cats' => $popular_ids, 'checked_ontop' => false ) ) ?>
            </ul>
        </div>
    <?php if ( current_user_can($tax->cap->edit_terms) ) : ?>
            <div id="<?php echo $taxonomy; ?>-adder" class="wp-hidden-children">
                <h4>
                    <a id="<?php echo $taxonomy; ?>-add-toggle" href="#<?php echo $taxonomy; ?>-add" class="hide-if-no-js" tabindex="3">
                        <?php
                            /* translators: %s: add new taxonomy label */
                            printf( __( '+ %s' ), $tax->labels->add_new_item );
                        ?>
                    </a>
                </h4>
                <p id="<?php echo $taxonomy; ?>-add" class="category-add wp-hidden-child">
                    <label class="screen-reader-text" for="new<?php echo $taxonomy; ?>"><?php echo $tax->labels->add_new_item; ?></label>
                    <input type="text" name="new<?php echo $taxonomy; ?>" id="new<?php echo $taxonomy; ?>" class="form-required form-input-tip" value="<?php echo esc_attr( $tax->labels->new_item_name ); ?>" tabindex="3" aria-required="true"/>
                    <label class="screen-reader-text" for="new<?php echo $taxonomy; ?>_parent">
                        <?php echo $tax->labels->parent_item_colon; ?>
                    </label>
                    <?php wp_dropdown_categories( array( 'taxonomy' => $taxonomy, 'hide_empty' => 0, 'name' => 'new'.$taxonomy.'_parent', 'orderby' => 'name', 'hierarchical' => 1, 'show_option_none' => '&mdash; ' . $tax->labels->parent_item . ' &mdash;', 'tab_index' => 3 ) ); ?>
                    <input type="button" id="<?php echo $taxonomy; ?>-add-submit" class="add:<?php echo $taxonomy ?>checklist:<?php echo $taxonomy ?>-add button category-add-sumbit" value="<?php echo esc_attr( $tax->labels->add_new_item ); ?>" tabindex="3" />
                    <?php wp_nonce_field( 'add-'.$taxonomy, '_ajax_nonce-add-'.$taxonomy, false ); ?>
                    <span id="<?php echo $taxonomy; ?>-ajax-response"></span>
                </p>
            </div>
        <?php endif; ?>
    </div>
    <?php
}

The first function is responsible for swapping the metabox callback on the default post_categories_meta_box for our new one.

The second function is basically a copy-and-paste of the original post_categories_meta_box callback, where I’ve modified the part that puts the selected categories on top.

Seems like a lot of work for something so basic, eh?