Another major issue would be that by the time this would happen the block rewards would likely be substantially lower then they are now (probably either 3.125 or 6.25 BTC plus tx fees per block) and having a lower amount of TX fees could compromise the security of the network as there would be less of an incentive to mine making it easier to execute double spend attacks.
3.125 BTC is more than 10% of the current block reward in bitcoin terms. If from "skyrocketing" you have in mind a rise of 10-fold or more then difficulty should in fact be higher than it is today.