Big is a highly relative term — you can use https://webpagetest.org to see what icons each browser downloads but it's exceedingly uncommon for a site to be so aggressively optimized that the icons are a substantial amount of what any given browser downloads and the content is non-blocking and trivially cached by a CDN. Almost any site can save at least one order of magnitude more data by removing a single JavaScript dependency.

The CIRA website (Canada's .CA domain authority) used to have a badly cached 2.5mb favicon, wasting plenty of bandwidth over the years until I caught it.

This is why there is “With just three PNG images in this minimum set, you can use advanced tools to optimize their size. It solves a problem for Internet users that don’t have unlimited data plans.” note later in the article

Browsers won't always download all available icons if they don't need to. To test a browser, open its network monitor and hard-refresh the page.

or bandwidth that would not be used otherwise - I guess though most sites nowadays would make that unlikely.