magento 2 remove shipping amount from cart total

I want to remove shipping amount from cart page because we do not provide estimate shipping amount calculation block.

Also, when customer add product to cart then its display grand total without shipping amount but if customer in checkout page and select shipping method and again back to cart page then cart grand total display amount including shipping amount and shipping method and amount not display here.

Please see below images.

For this I have override cart index controller in custom module and code is as below.

1) app/code/Hs/Mageenhancement/etc/di.xml

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
    <preference for="MagentoCheckoutControllerCartIndex" type="HsMageenhancementControllerCartIndex" />
</config>

2) app/code/Hs/Mageenhancement/Controller/Cart/Index.php

    <?php

namespace HsMageenhancementControllerCart;

class Index extends MagentoCheckoutControllerCartIndex
{
    /**
     * Shopping cart display action
     *
     * @return MagentoFrameworkViewResultPage
     */
    public function execute()
    {
        $quote = $this->_checkoutSession->getQuote();
        $shippingMethod = $quote->getShippingAddress()->getShippingMethod();
        if($shippingMethod){
            $quote->getShippingAddress()->setShippingMethod(null);  //setting method to null
            $quote->save();

            $quote->collectTotals();
            $quote->save();
        }
        $resultPage = $this->resultPageFactory->create();
        $resultPage->getConfig()->getTitle()->set(__('Shopping Cart'));
        return $resultPage;
    }
}

I have used same below technique in Magento 1 and its working fine but in Magento 2 its not working.

$quote = $this->_checkoutSession->getQuote();
        $shippingMethod = $quote->getShippingAddress()->getShippingMethod();
        if($shippingMethod){
            $quote->getShippingAddress()->setShippingMethod(null);  //setting method to null
            $quote->save();

            $quote->collectTotals();
            $quote->save();
        }

Please help me how to remove shipping charge in cart page.