Lets conduct a scifi thought experiment, and talk about Bitcoin at a requirement level assuming some magical quantum scifi tech that can make it real sometime during the next 100 years: using the really high level definition that Bitcoin is a global process of converting electricity into some physical coin via transmogrification/energy to physical object or sufficiently advanced scifi to look like magic today, and its called a bitcoin and it can be easily inspected to see how many Joules it took to make (and the time at which it was made); and where all of these bitcoins are produced globally such that the process somehow magically knows (via non-local quantum communication?) the number of bitcoins created globally and the Joules/bitcoin consumed and which then adjusts the Joules/proof required to produce bitcoins over time to hold production interval on target at 10mins every 2016 blocks, starting with 50 bitcoins from its earlier incarnation before a few upgrades, origination back in 2009, and then halving every 4 years and currently running ag 11.921bits/per block. Its all a bit scifi but maybe the coin contains a globally unique proof of work, its somehow magically turing universal and cryptographic AI and it doesnt matter what algorithm is used for the proof and any will be accepted, just the mining is an optimally efficient process, and what counts is the amount of electricity used, and the verifier can understand and easily verify any proof (and obviously the AI is going to see through any short-cuts).
When you look at it like that, the 2015 bitcoin cant quite do that global non-local communication, universal cryptographic AI nor electricity to matter transmogrification, but thats really just an implementation limitation, that maybe we can fix with quantum sci-fi in the next 100 years future, and the current bitcoin is a pretty close facsimile.
One day a fellow named Bob had an idea, he could stamp an F on the bitcoins and call them foocoins and persuade people they were better! He choose some different interval of parameters and split the bitcoins into different sizes and stamped F on top them and talked up a good spiel so that others started playing too.
However they were still fractions of actual bitcoins because the proof is universal due to the cryptographic AI, there was nothing Bob could do that could change that fact, no supply parameter changes, hash function used, software feature, not even a retro pacman game (loaded into the FHE processor in the coins), branding etc would change that because the universal cryptographic AI was measuring Joules expended, and unlike humans was not easily swayed by marketing and logos: a proof of joules mined is a proof joules mined, whatever letter or logo you stamp on the coin!
Because it started at difficulty 1 and ideal quantum processors are fast, foocoin difficulty adapted really fast (2016 blocks were over in a femtosecond), but as few found Bobs ruse plausible difficulty stabilised and by some creative marketing Bob found he could sell smaller and smaller fragments of bitcoins with F stamped on them and exchange them for whole bitcoin. As this was profitable Bob and his friends ramped up production and used the proceeds to go on a marketing drive!
One day some people started complaining that these coins were F crazy because they were the same material as bitcoin, in fact they were bitcoin, but Bob was selling them above par and they started demanding their money back. Naturally Bob had spent a lot of the money on marketing and flashy objects. The price crashed to true value, which unfortunately for the holders was really close to zero. Bob made some money, but unfortunately he didnt hide his identity very well and he was convicted and given some community service and had to make reparations (it seems pyramid scams and stock pump & dump scams and currency skimming/debasement are still illegal in the 22nd century.)
We have that same problem in current times. The universal AI is called common sense: changing hash functions does not change the joules expended per coin, a hash with half the gate count results in a difficulty twice as high but the same Joules/coin. A hash with a lower power density (say because it uses more RAM) can be run at a higher clock rate within thermal limits, and still use the same Joules/coin. Changing the supply function to 2x as many coins doesnt change the value it halves the price expressed in 1/2 bitcoins. Having a shorter halving schedule just makes the price change to 4x as many coins at price expressed in 1/4 bitcoin after the earlier halving etc. The pacman game doesnt change things either because if it was useful to play pacman on bitcoin, someone would fork the code and add it; an arms race of cutting and pasting each others code doesnt create value. Chances are the reason bitcoin doesnt have a pacman game is it isnt that useful or you dont need bitcoin to play pacman. The 2015 Bitcoin doesnt yet know about users mining coins stamped with creative logos is because it lacks quantum non-local communication, we'll fix that one day, but in the mean time humans can convert one supply function to another with simple math and measure average electrical efficiency and when measured this way people are paying way over par, no rational entity would put money into marked coins, never mind a cryptographic universal AI.
A bitcoin is a proof of Joules spent, no matter what branding or features you market with a bitcoin its still a bitcoin, and can no more change than a clump of gold atoms will cease to be gold atoms and start a floating price against gold if stamped with a letter F (assuming free instant assay like bitcoin has).
Adam