The factor of 1/683 - that's to make the physics-based definition of the candela consistent with older definitions. That is where the human vision system peaks. The use of 540 terahertz in the definition of the candela is anything but arbitrary. People make mistakes in low lighting, get headaches in overly bright lighting.
We need artificial lighting to make our modern world possible. It exists to support humans, and in particular, commerce and industry. The SI doesn't exist to support the sciences that it does support the sciences is a nice side benefit. The right question: Why do these standards (any of them) exist? The answer is commerce and industry. Is there any rationale from the standpoint of physics to choose candela as a base SI unit? That just means, though, that we need to up our game a bit and realize that there's an extra dimension at play here - the subjective sensation of brightness as perceived by the human eye as a measuring device - that we need to include on an equal footing to our clocks, meter sticks and (soon to be) watt balances, if we really want to produce measurements which are useful in a world inhabited by humans. Similarly, it's easy to simply slide over terms like photometry and not realize that it's very different to radiometry. It is very easy, as a physicist, to simply give up and reckon that "luminous intensity" will simply be one of the list. When measuring the "brightness" of a light source, there is a huge number of different quantities of interest, each with their own unit but a very similar name to the others, and depending on exact details like whether you're integrating over angle, or surface, or wavelength, or any combination thereof. The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\cdot10^(\lambda)$ using only comparative measurements of (perceived) luminous intensity, which are much easier.
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