Can I make a taxonomy meta box into dropdowns for each parent category?

You need to dive in the wp_dropdown_categories( $args ); and wp_list_categories functions to list your terms, even if I don’t think it’s the better way. For accordion you will need to compose your own select and option entries and use your own css/js like Smooth accordion dropdown menu.

It’s possible to list term hierarchically with wp_dropdown_categories( $args );.

the list of args to change as you want :

$args = array(
    'show_option_all'    => '',
    'show_option_none'   => '',
    'option_none_value'  => '-1',
    'orderby'            => 'ID',
    'order'              => 'ASC',
    'show_count'         => 0,
    'hide_empty'         => 1,
    'child_of'           => 0,
    'exclude'            => '',
    'include'            => '',
    'echo'               => 1,
    'selected'           => 0,
    'hierarchical'       => 1,
    'name'               => 'cat',
    'id'                 => '',
    'class'              => 'postform scrollable-menu',
    'depth'              => 0,
    'tab_index'          => 0,
    'taxonomy'           => 'category',
    'hide_if_empty'      => false,
    'value_field'        => 'term_id',
);
wp_dropdown_categories($args);

To make the select dropdown scrollable,

.scrollable-menu {
    height: auto;
    max-height: 200px;
    overflow-x: hidden;
}

Hope it helps you !