Is it just to give it a better look when seen from the top down?
Pretty much. I believe it’s so that the light hitting the gem from various angles gets reflected out the top, making it extra-sparkly.
There are lots of different diamond cuts. The classic “diamond” shape is the brilliant cut, of which there are lots of variations. The basic idea is to maximise the amount of light reflected internally back out through the top face, thus more sparkle. 
To add…when a diamond is cut correctly, almost all the light that enters the top gets reflected back out the top and scattered by the facets, you see the brilliance of the light being reflected. The opposite would be a flat bottom, which would act like a window, and all you would see is the shadowed base of the ring. Having the pointy bottom makes the light reflect back up instead of passing through, like a flat bottom would.
As a side note, when I look at a diamond, I generally am looking at the clarity(flaws) and color, but also whether it has an open culet(truncated bottom) or not. The idea of a diamond coming to a point at the bottom usually indicates it’s a modern round brillian cut, made sometime after 1940 or so. Prior to that they were mostly truncated on the bottom and indicate a pre-WWII European cut or modified European cut.
I think it may also be that we’ve come to expect that diamonds have that shape. If a jeweler were looking at “introducing”* a new shape, one that didn’t come to a point (and was also less sparkly), it just wouldn’t sell. It’s not what we expect, or have come to desire in a diamond.
*I know that shape isn’t new, as mentioned above, but from a market standpoint, that would quite possibly be how they phrase it.
It;'s also important that it used to be that diamonds could only be cleaved (“cut”) along the crystals fracture planes, and that any shape you wanted to make a diamond required that it be possible to do by using those planes. That limited the type and number of shapes possible. Combine that with the desire to make a shape that will take advantage of a diamond’s huge refractive index (2.42, one of the highest for a natural solid in the visible) and its high dispersion, and you’re lead to something like the present shape.
It’s only in the past 50 or so years that they’ve come up with abrasives harder than or as hard as diamond that you could use to grind and polish non-cleavage faces on diamond.
One of the most pleasing “natural” shapes for a diamond, by the way, is an octohedron, which is literally “diamond shaped” (as in the figure on a suit of cards), and gives that rhomboid shape its name.
Really? What are they? I thought nothing was harder than diamond (though some things, like silicon carbide, can get close).
Look up miners cut diamonds. The change to a pointed pavilion rather than a flat one deals with a better understanding of how the facets reflect light, particularly is the fire of the diamond dependent on light coming through the pavilion or light going through the table and then reflected back out.
Anyone who’s played with Photoshop for more than ten minutes can tell you exactly where brown falls in the spectrum.
Paste gems, rhinestones, etc. may not have points on the bottom, especially if stuck to surfaces like Elvis’s costumes. Light would pass out the bottom in that case, so the bottom is “silvered” with metal such as tin, or nowadays plastic like mylar.