Do you see your equation?
1 bitcoin = 1 bitcoin is like saying this
1 inch = 1 inch
1 pound = 1 pound
1 byte = 1 byte.
That is not how units work! The are all equal to something that is objectively real.
If that is sound reasoning I must be fucked in the head.
I'm currently in my third year of a Chemistry-Physics degree, so I'm actually quite familiar with units. Don't worry, you're not fucked in the head, your reasoning is just slightly off.
Let me give you an example of a time when we made a change to our definition of a very common unit:
The metre, a well know unit of measurement, was once defined by a standard platinum bar. The bar was created to act as the universally agreed upon definition of 1 metre, and was therefore
by definition exactly one metre long. This was consistent to within a certain degree, but of course changes in e.g. temperature/pressure could in fact cause the length to vary slightly. Parameters were introduced to improve the consistency (specific temperature and pressure at which the length of the bar would considered to be exactly one metre) but unfortunately, using a physical object to act as a benchmark can never be as accurate as the scientific community would like.
It was therefore decided that we should redefine the metre, without using a physical object. Einstein had shown, in his theory of relativity, that the speed of light is in fact a universal constant when measured within the same medium. It therefore made sense to redefine the metre in terms of this unchanging physical constant. Our definition of the metre is now 'The length of the path travelled by light in a vacuum in 1⁄299,792,458 of a second'
Your idea that units must be 'equal to something that is 'objectively real', while it may seem somewhat intuitive, is actually a slight misunderstanding. The fact that it is so difficult to find consistency in objective reality is what makes the task of measuring things so tricky.
Back to Bitcoin:
Bitcoin is actually a great starting point if we want to define a system of measurement for value. What we are effectively doing is defining a standard unit of value, i.e. 1 bitcoin, which can act as a universal constant similar to the speed of light in the example above. Now we have our benchmark (which doesn't fluctuate due to changes in temperature/pressure etc.), and we can start to decide how to value everything else in comparison to it. (notice that making measurements always boils down to making comparisons between things)
Of course, being so new, and being introduced to a society who are so used to valuing things in a different way (namely whichever fiat currency they grew up with), make things more complicated (as well as a million other things, economics can't really be compared with science due to the numerous factors to consider, but we're talking about units here). We are still in price discovery phase with people having to shift their perspectives and adjust. It is yet to be seen whether or not the population as a whole will accept this new measurement system.
The problem of making measurements and defining units is and always had been at the heart of the scientific discipline. Its an interesting subject, and there's a great deal of understanding to be gained by studying it in a bit more depth.