Our routing system stores the processed URLs into Router::$cache so that it does not have to handle building process more than one time for the same URL. Please note that this is in memory cache, data in Router::$cache are the URLs for each page load. In real life usages, there won't be that large number of URLs per page, so I think the current implementation is fine.

Since this is in memory cache for each page load, I think the solutions you suggested are not applicable, too.

Yes, it is fine for general real-life usage.
But in my case, there are more than three million pages on my website.
I have a CLI app in Joomla to build a sitemap.
Router::$cache is a protected variable, so I can't access it directly.
I have to remove or disable that cache in my app.
How can I override class Router or class SiteRouter?

You can create a system plugin which loads your version of the router class either during construction of the plugin object or on the event onAfterInitialise. We will not remove the cache for the router in the CMS by default.

@Hackwar Could you please provide an example code which allows loads your version of the router class ? That would help users who has similar requirement.

<?php
use Joomla\CMS\Plugin\CMSPlugin;

class plgSystemMyownrouter extends CMSPlugin
{
	public function onAfterInitialise()
	{
		require_once __DIR__ . '/router.php';
	}
}

And in the router.php you have your copy of the router class.

Thanks !