As many of the SharePoint users, you too like the old classic experience and you are using these switching functionality heavily?
How does it work?
Microsoft internally is going to save a cookie in your browser called splnu as shown below;
If the cookie does not exist or it contains value of 1 which means you are in modern experience. Value of 0 indicates a classic experience.
Many times we notice the link does not appear at all as shown below;
To bring the default functionality back, please open the browser developer tool and run following command from console;
document.cookie = "splnu=0;domain=" + window.location.hostname + ";"; location.href = _spPageContextInfo.webServerRelativeUrl + "/_layouts/15/viewlsts.aspx";
Now you should see your switch back. Happy switching!