One of the issues with bitcoin is that it is has a constantly changing price over time.
This creates large
menu costs. This is where people have to constantly adjust their prices to keep things aligned.
Difficulty and price tend to be well aligned. Over the long term, cost of electricity, hashing hardware and other optimisations have an effect. However, it is reasonably slow.
From
this spreadsheet, the price vs difficulty ratio has been reasonably constant. Any deviations will cause more hashing to come online or switch off.
1 BTC is equal to 100 million Satoshi, so maybe the unit could be 100 million divided by the difficulty. The difficulty is currently 9 million, so 1 unit would be equal to 11.1 BTC. If difficulty increases, then so would the value in the wallet.
The graph calls the ratio the "Solex Factor", so maybe the unit could be called the Solex or Sol or something.
Merchants could price their stuff in Sols and the variation would be around the same as other fx trading. Users would see their Sol total increase over time on the client as the value of the BTC changes.
There would need to be a warning that the BTCs are "real" and the Sols are just a guideline of value.
The BTC vs $ price varied from 5 cents to $70 and the $ to difficulty only varied slightly. The peak was 60% higher than the trough.