Thanks for your interest.
I will try to answer the why first.
The purchase of physical gold is not always legal, feasible, encouraged or easy in many jurisdictions and parts of the world.
The purchase of gold bullion and coins is fraught with having to assay them and verify their authenticity and purity.
The average man would have to purchase a safe or worry about hiding it.
Transporting gold is arduous, especially across borders or distance.
Gold in the form of a decentralized (distributed) open source and free (as in freedom) cryptocurrency might encourage people to use both gold and cryptocurrencies.
I am sure there are many more reasons.
How would I attempt it?
A community of like-minded people would start a project aimed at creating this gold pegged cryptocurrency and I stress that it be pegged to gold but not backed by gold.
First issue the coin with a fair distribution – maybe an ICO of a reasonable amount of coins which are mined just to get it off the ground. The mining of transactions and regular mining like Bitcoin's proof of work to be alternated between mining the coins and transactions and mining only the transactions with burn of half the transaction fee accordingly:
If for example our coin @ $1500 is trading higher than gold @ $1100 we increase the quantity of our coin by enabling 'mining' until the price approaches that of gold.
If for example our coin @ $300 is trading lower than gold @ $1100 we first wait to see if price rises on its own (its supposed to be pegged to the price of gold so there might very possibly be those that will buy in anticipation of the rise and thereby push the price up making any further measure redundant in this scenario) and if it does not rise, we halt the issue of our coin by disabling mining and miners would be paid only to verify transactions and this would halt inflation. Finally if even then, the price fails to rise ,we would destroy some of the supply by means of paying half of the tx fees to the miners
and the other half of the transaction fee would be destroyed and in effect cause deflation and scarcity thereby bring up the price.
Initially the coin would probably be volatile and would have a loose peg. Prices would rise and fall
which would be good opportunity for speculators, however , with time the price should stabilize
with wider adoption.
The idea is control the quantity and you have done it with only one coin. Decisions on when to each measure should be taken should be reached by consensus of the community. Maybe something like what Dash is doing.