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The techniques detailed on the page (reweighting lines, removing fine details) seem like a worthwhile reason to at least use a different file for the "tiny" image. Unless SVG renderers start using those techniques at a small enough size.

It looks like only Firefox or Opera would support an SVG favicon: https://en.wikipedia.org/wiki/Favicon#File_format_support

This is for favicons, where svg support is pretty spotty.

Even with svg, they ultimately become rasters once they are on the screen. So for favicons it might still be beneficial to control the scaling yourself with a tool like this.

The techniques (for example, removing fine details) are applicable to SVG too.