Remove parent term selector for hierarchical taxonomies

plugin.php

/**
 * Fool WordPress into thinking this taxonomy isn't hierarchical so it doesn't show the parent dropdown on the add/edit term page
 */
function disable_parent_category_dropdown() {
	global $wp_taxonomies;

	$wp_taxonomies['my_taxonomy']->hierarchical = false;
}
add_action( 'my_taxonomy_pre_add_form', 'disable_parent_category_dropdown' );
add_action( 'my_taxonomy_pre_edit_form', 'disable_parent_category_dropdown' );

/**
 * Reverse the previous change after the add/edit term form
 */
function disable_parent_category_dropdown_reverse() {
	global $wp_taxonomies;

	$wp_taxonomies['my_taxonomy']->hierarchical = true;
}
add_action( 'my_taxonomy_add_form', 'disable_parent_category_dropdown_reverse' );
add_action( 'my_taxonomy_edit_form', 'disable_parent_category_dropdown_reverse' );

/**
 * Remove the parent dropdown when adding a term from the edit post screen (non-gutenberg)
 */
function disable_post_parent_category_dropdown( $args ) {
	if ( $args['taxonomy'] === 'my_taxonomy' ) {
		$args['echo'] = false;
	}

	return $args;
}
add_filter( 'post_edit_category_parent_dropdown_args', 'disable_post_parent_category_dropdown' );