Water is used because it is universal, and pure water is used because it is easy to make through distillation. Brine must be of a specified salt, and the salt must be itself pure, both of which complicate things needlessly. Then the brine would have to be fully saturated to be consistent, and that varies with temperature- more complication.
Elevation of course lowers the boiling point, but that can be corrected mathematically.
I don't see how using a known, consistent, reproducible reference is arbitrary, except that any type of measurement can be considered arbitrary on some level.
I am only disagreeing with the use of "arbitrary." Otherwise, I quite agree with you.
An aside: living in a country that primarily uses Fahrenheit and other non-metric scales, I obviously have difficulty interpreting the more logical measures in day-to-day life because of what I am used to, familiar with, and exposed to. I do, however, find metrics far more logical. When reading scientific studies (which I sometimes do for fun), or mixing photographic chemicals (I suppose also recreationally), metrics are easier for me. If you tell me the outside temperature in F, I know if I consider it comfortable. When someone in Europe posts the temperature in C, I have to cross-reference. I would be fine if the U.S. finally completed its conversion to metric, though would feel nostalgic for what I'd grown up with.
The best way to do things is, as you say, to use a known, consistent, reproducible reference. The Fahrenheit scale (and others) have also done this. However, there is nothing written by any deity on any stone tablets or flaming letters on a mountain stating what that reference must be, or what the 0 and 100 points must be (or whether those numbers must be used at all). It had to be standardized on something, and what was chosen was abundant and _easy_ (relative to other choices - though I'm sure a chemist would prove me wrong). Water should be "pure," etc., to be consistent; and "pure" water is not universally available on this planet without complicating things.
Absolute zero is less arbitrary (though still theoretical) - it is the cessation of molecular activity and has nothing to do with what kind of molecules we standardize on. Of course, one could argue it's still arbitrary, lol.
Just because it is now a standard, and we (presumably) agree a good and logical one, does not mean it is not arbitrary, that is all.
Tangentially related to onanism, they had statuary back when these scales were created, so 0 could have just as easily had something to do with a brass monkey. Actually, there are circles around here where the brass-monkyometer does seem to be an unofficial standard.