All do respect intended I agree wholeheartedly with @OsyenVyeter. I don't see the point at all.

It's a way of retaining control of distribution.

1. Before this feature was added, non-FontStructors would often download fonts, then upload them to various "1,000 FREE-FREE-FREE FONTS !!!!" websites.  Sadly, all too often the uploader would either claim to the creator of the font and/or remove the creator/attribution information -- which were against the creator's wishes and copyright claims.

The creator would then have to scour these sites, contact the owner, and make a claim for removal -- all of which take time and effort for something that was not their doing in the first place.

2. FontStructors may also choose to sell their fonts; a few FontStructors would make an initial font, then upgrade them to a more 'professional' version using FontStruct.  By removing the Download option, the prospective customer could still view the font and test it out before purchasing it, usually by contacting the FontStructor.

The other alternative was to remove key glyphs to make it a demo font.  A few days ago, someone asked, "Why is each letter $8?" after discovering one of these older font demos.  This was how FontStructors were forced to sell fonts prior to the No Download option.

(P.S. At the time, it was $8 for that particular font, not $8 for each letter.  It was placed in each missing glyph so as to not be overlooked or missed.)

3. Still others make and/or use their fonts for personal or commercial use, but also want to display them as a form of creative artwork from which others may take inspiration.
 

Sorry: "...claim to _BE_ the creator of the font..."