Well I don't think I'd want the increased price to persist through your opponent's turn. To me, it's fundamentally important that Copper costs $0, since it means that no matter is done, at least you can buy a Copper. Then even under relentless militia attacks, three Copper buys Silver, three Silver buys Gold, and 1xSilver + 2xGold buys Province (three Gold buys Platinum, and 2xGold + Plat buys a Colony). If you up the price of Copper for opponents, then you open the door to pinning.
Sure, the basic treasure piles can run out, but that's just because it's a physical game. The intent is clearly that the piles won't empty, except under rather extreme conditions.