Add module.xml file in app/code/Magemonkeys/ShippingHide/etc and copy the following code in it:

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
	xsi:noNamespaceSchemaLocation="../../../../../lib/internal/Magento/Framework/Module/etc/module.xsd">
    <module name="Magemonkeys_ShippingHide" setup_version="2.0.10">
        <sequence>
            <module name="Magento_Shipping"/>
        </sequence>
    </module>	
</config>

Add registration.php in app/code/Magemonkeys/ShippingHide and copy the following code in it:

<?php
MagentoFrameworkComponentComponentRegistrar::register(
    MagentoFrameworkComponentComponentRegistrar::MODULE,
    'Magemonkeys_ShippingHide',
    __DIR__
);

Add Uninstall.php file in app/code/Magemonkeys/ShippingHide/Setup and copy the following code in it:

<?php

namespace MagemonkeysShippingHideSetup;

use MagentoFrameworkSetupUninstallInterface;
use MagentoFrameworkSetupModuleContextInterface;
use MagentoFrameworkSetupSchemaSetupInterface;
use MagentoConfigModelResourceModelConfigDataCollectionFactory as ConfigCollectionFactory;

/**
 * ShippingHide Uninstall
 */
class Uninstall implements UninstallInterface
{
    /**
     * Config Collection Factory
     *
     * @var MagentoConfigModelResourceModelConfigDataCollectionFactory
     */
    private $_configCollectionFactory;

    /**
     * Initialize Setup
     *
     * @param ConfigCollectionFactory $configCollectionFactory
     */
    public function __construct(
		ConfigCollectionFactory $configCollectionFactory
	) {
        $this->_configCollectionFactory = $configCollectionFactory;
    }
    
    /**
     * Uninstall DB Schema
     *
     * @param SchemaSetupInterface $setup
     * @param ModuleContextInterface $context
     * @return void
     */
    public function uninstall(SchemaSetupInterface $setup, ModuleContextInterface $context)
    {
        $setup->startSetup();
        $this->removeConfig();	
        $setup->endSetup();
    }

    /**
     * Remove Config
     *
     * @return void
     */
    private function removeConfig()
    {
        $path = 'shipping/behavior';
        /** @var MagentoConfigModelResourceModelConfigDataCollection $collection */
        $collection = $this->_configCollectionFactory->create(); 
        $collection->addPathFilter($path);

        foreach ($collection as $config) {
			$config->delete(); 	
        }
    }    
}

Add config.xml file in app/code/Magemonkeys/ShippingHide/etc and copy the following code in it:

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
	xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Store:etc/config.xsd">
    <default>
        <shipping>
            <behavior>
                <hide>1</hide>
            </behavior>
        </shipping>		
    </default>
</config>

Add di.xml file in app/code/Magemonkeys/ShippingHide/etc and copy the following code in it:

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
	xsi:noNamespaceSchemaLocation="../../../../../lib/internal/Magento/Framework/ObjectManager/etc/config.xsd">
	<!-- plugin -->		
    <type name="MagentoShippingModelRateResult">
        <plugin name="Magemonkeys_ShippingHide" type="MagemonkeysShippingHidePluginShippingModelRateResult" />
    </type>
</config>

Add system.xml file in app/code/Magemonkeys/ShippingHide/etc/adminhtml and copy the following code in it:

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
	xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Config:etc/system_file.xsd">
    <system>
        <section id="shipping">
	   <group id="behavior" translate="label" showInDefault="1" showInWebsite="1" showInStore="1" sortOrder="310">
                <label>Behavior of Methods</label>
                <field id="hide" translate="label comment" type="select" sortOrder="10" showInDefault="1" showInWebsite="1" showInStore="1" canRestore="1">
                    <label>Hide Mode</label>
                    <comment>Hides any other shipping methods if free shipping is available.</comment>
                    <source_model>MagentoConfigModelConfigSourceYesno</source_model>
                </field>
            </group>
        </section>
    </system>
</config>

Add Data.php file in app/code/Magemonkeys/ShippingHide/Helper and copy the following code in it:

<?php

namespace MagemonkeysShippingHideHelper;

use MagentoStoreModelScopeInterface;
use MagentoFrameworkAppHelperAbstractHelper;

/**
 * Shipping Hide Helper
 */
class Data extends AbstractHelper
{
    /**
     * Enabled Config Path
     */
    const XML_CONFIG_ENABLED = 'shipping/behavior/hide';
 	
    /**
     * Check Hide mode Functionality Should be Enabled
     *
     * @return bool
     */
    public function isEnabled()
    {
        return $this->_getConfig(self::XML_CONFIG_ENABLED);
    } 

    /**
     * Retrieve Store Configuration Data
     *
     * @param   string $path
     * @return  string|null
     */
    protected function _getConfig($path)
    {
        return $this->scopeConfig->getValue($path, ScopeInterface::SCOPE_STORE);
    }      
}

Add Result.php file in app/code/Magemonkeys/ShippingHide/Plugin/Shipping/Model/Rate and copy the following code in it:

<?php

namespace MagemonkeysShippingHidePluginShippingModelRate; 

use MagemonkeysShippingHideHelperData as ShippingHideHelper;

/**
 * Shipping Result Plugin
 */
class Result
{   
    /**
     * Helper
     *
     * @var MagemonkeysShippingHideHelperData
     */
    protected $_helper;
    
    /**
     * Initialize Plugin
     * 
     * @param ShippingHideHelper $helper
     */
    public function __construct(
        ShippingHideHelper $helper
    ) {
        $this->_helper = $helper;
    }
        	
    /**
     * Return all Rates in the Result
     *
     * @param Result $subject
     * @param Method[] $result
     * @return Method[]
     */	
    public function afterGetAllRates($subject, $result) 
    {
        if (!$this->_helper->isEnabled()) {
            return $result;
        }       		
		$rates = $this->getAllFreeRates($result);              
        return (count($rates) > 0) ? $rates : $result;
    }	
        	
    /**
     * Return all free Rates in the Result
     *
     * @param Method[] $result
     * @return Method[]
     */	
    public function getAllFreeRates($result) 
    {	
		$rates = [];
        foreach ($result ?: [] as $rate) {
            if ($rate->getPrice() < 0.0001) {
                $rates[] = $rate;
            }
        }               
        return $rates;
    }	    
}

Run CLI Commands

rm -rf var/di/* var/generation/* var/cache/* var/log/* var/page_cache/* var/session/* var/view_preprocessed/* pub/static/*
php bin/magento setup:upgrade
php bin/magento setup:upgrade
php bin/magento setup:static-content:deploy -f
php bin/magento cache:clean
php bin/magento cache:flush

Result

No method of free shipping

There is a method of free shipping