Why pure water? Probably because it's the most common solvent in the world, and integral to life as we know it. And we can consistently make it.
Why not water at the average saltiness of the ocean? To complicated
1) It's a lot easier to produce "pure" water than it is to adjust the salt content of water to match the average
2) There is more variation than you would think in the saltiness of the ocean - which would require a lot of sampling, and as we did more sampling, the scale would change, or it would become the average of samples at these 46 points done on this day in 1724.
3) There is a lot more than just NaCl in the ocean, and you'd have to match that exactly
4) You'd still have to produce pure water first to reliably create your standard for "sea water" in a lab.
Why sea-level (1.0 ATM / 14.7PSI / etc.)? Probably because it's easy to define and check (it just requires a consistent work).
Compare that to Fahrenheit, which was originally defined by two end points, the freezing point of a fully saturated solution of water and salt (probably at 1 ATM) as 0'F; and human body temperature as 100'F (of course a human's nominal temps differ to the point that we now expect 98.6'F as your body temperature).
Coincidentally, Fahrenheit is now defined by the freezing and boiling points of pure water (at 1 ATM) and pegged at 32'F and 212'G for purely "arbitrary" reasons.