The reason you need Google Tag Manager for your website is because the Google Tag Manager gives you the ability to add and update your own tags for conversion tracking, site analytics, remarketing, and more.
There are nearly endless ways to track activity across your sites and apps, and the intuitive design lets you change tags whenever you want.
Google Tag Manager is a tag management system (TMS) that allows you to quickly and easily update measurement codes and related code fragments collectively known as tags on your website or mobile app.
The most common use case for installing a tag on your website is to gather data for a digital analytics solution.
When someone visits your site, that tag shares data about that visit with your analytics server so that your analyst can make recommendations to improve site performance or optimize marketing campaigns.
At least based on my experiment, GTM does indeed help sites load a bit faster (comparing to the test where the same tags were hardcoded).
But this is NOT categorically true in every case.