If due to this by-design artificial scarcity the dollar price of BTC increases 10,000x, then by definition the value of us dollars has decreased by 1/10,000. If BTC is to be the only decentralized crypto-currency and be used by everyone, then the net worth of the broad population must become devalued by 1/10,000.
After only a small percentage of the broad population has purchased Bitcoin, the price will be several doublings higher than it is now and the net worth of rest of the broad population will be devalued by the reciprocal of several doublings. Five doublings is 32x. Bitcoin has already risen from pennies to $350, which is roughly 15 doublings.
While the value of dollars relative to Bitcoin will drop, the value of the dollars themselves won't change very much. For example, dollars will still buy about the same amount of gold, the same number of apples, the same number of Euros, and so on.
Bitcoin can only capture value it creates. Alternative currencies will have to create value in order to capture it.