Feature Request

Hmm, that is a possibility I suppose. It would get tricky as you need to target a specific shipping method. So with UPS, you’d need to choose which exact method.

As an example, here is a short snippet for adding a cost onto FedEx Ground:

function add_cost_to_shipping_rate( $rates, $package ) {
    $extra_cost  = '10';

    if ( isset( $rates['fedex:FEDEX_GROUND'] ) ) {
        $rate = $rates['fedex:FEDEX_GROUND'];
        $rate->cost = $rate->cost + $extra_cost;
    }

    return $rates;
}
add_filter( 'woocommerce_package_rates', 'add_cost_to_shipping_rate', 10, 2 );

I don’t think this is something suitable for the plugin’s core code, but I can add in a filter to allow you to stop the fee from being added and use the cost of the fee in a custom snippet like the above to add to a shipping cost.