First ID won’t be excluded in wp_dropdown_pages with an $arg from tax_query

You don’t need to add single quotes before using $exclude. Literals are enclosed in quotes to show it’s a string, but since $exclude is already a string variable, you can pass it directly.

Remove $excluded, you don’t need it at all and just use

$ogpk_pickup_field_args = array (
        'depth' => -1,
        'class' => 'store-pickup form-row-wide',
        'show_option_none' => __( 'Choisissez le point relais où retirer votre panier', 'organic-pickup' ),
        'name' => 'store_pickup',
        'hide_empty' => false,
        // 'exclude' => '1074,1072,1059',
        'exclude' => $exclude,
        'post_type' => 'organic-pickup',
        'value_field' => 'ID',
        'suppress_filters' => true
    );