The triple point is actually, 0.01°C, now fixed at that value by definition, making 0.01°C a datum point, not 0°C as commonly believed. Until about 60 years ago 0° was the freezing point of water, and 100° was the boiling point of water at sea level when the barometric pressure was exactly 101.325 KPa. Recognizing that this definition was problematic (but unable to admit for whatever reason that Fahrenheit was brilliant and had a better way, or maybe because the old wives tale about armpit temperature just would not die, it was not a datum point for his scale, just a coincidence.) the international commission of standards redefined the scale.
Today the scale is defined by absolute 0 and the triple point of water. Not just any water, but a formulation of water containing specific isotope ratios known as mean standard ocean water. Then to set the scale, the triple point was fixed by definition at 273.16K and a degree is 1/273.16th of the difference between the two. The Celsius scale is then defined in relation to this with -273.15°C = 0K by definition. Notice the .01° shift, which makes the triple point 0.01° on the Celsius scale. While the new definition is vastly improved and removes the pressure problem from determining the scale datum point, it introduces a need for sophisticated equipment to measure absolute zero and the triple point of mean standard ocean water. Additionally, it is dependent upon an exact formulation of water. Its also more difficult to divide a distance on a thermometer into 273.16 equal parts than it is to bisect it five times. The former is dependent upon having a measurement scale, the latter is not.
IMO, even had the F scale won out, we would have still tweaked the definition to improve its accuracy. But as long as 0° and 32° were the datum points, anyone with a bucket, ice, ammonium chloride, and a compass divider could have produced it with reasonable accuracy anywhere in the world.
That's probably more pedantic rambling about history than you wanted to know and history is full of what ifs. Its now what we have. In a modern first world country it doesn't really matter anymore and standardization is more important, so in the end, the Fahrenheit scale really needs to go the way of the Dodo bird. Now don't get me started on the foolish US public's intransigence over adopting the the SI standard and getting with the program. It's just plain stupid on our part and it hurts us economically and scientifically.
Gripe over, this thread has gone far enough off topic.