Backing and pegging are similar in that they both influence the price.
Backing protects the value from falling but it does not prevent the price from rising. Pegging stabilizes the value in both directions. Backing also does not require active intervention in the market, as demonstrated with silver dollars. The backing is connected to the currency when it is created. Pegging requires active management over the lifetime of the currency. Whether this is manipulation or "free market" is somewhat beside the point. What matters is if it's practical and trustworthy.
As I said, a ceiling is fairly straightforward to implement to prevent the price from rising. You could instill great confidence that the value will not rise above a certain level. But this is not the purpose of backing, and it is only half the purpose of a peg.
How to provide a price floor? Preventing bubbles will reduce volatility but it will not provide a minimum value.
if no new currency can enter the market while the price is suppressed, and you expect demand to pick up in the future, there is an incentive to buy more of the currency when it is low.
The problem is precisely falling value when there is not an expectation that demand will pick up.
There is also a confusion between supply as interpreted as the rate of money creation, and the supply as interpreted as the amount of existing money. The rate of money creation can be curtailed to zero, but the amount of money in existence won't shrink. If the amount of currency that people want to hold is less than the amount that exists, then the value will fall. Stabilizing the value with variable creation only works when the demand for existing money is growing.
If the demand for money is shrinking and there is not an expectation that the value will go up, then there is not money to be made by gobbling up all the excess currency at an above-market rate, holding it until the price exceeds parity which is expected to be never. Markets do not peg currencies automatically because currency peg must by nature oppose the market.