Sabatons are foot armor worn by knights, and they look rather like this:
Image source: Project Gutenberg via Wikimedia commons.
As you can see they have quite the point - and bizarrely, historians are not sure why other than "fashion."
It's actually quite obvious to a horse person. Cowboy boots and many tall English boots also have points, although not as much as that. While wearing armor, the knight's ankle is supported but motion is restricted - the point helps get the foot into the stirrup and regain a lost stirrup. Paddock boots do not have the point - but you can move your foot much more in them (trust me).
So, no, the point is not fashion. It's sharpness is probably to provide an extra weapon in close combat.