You don't even need a softfork to issue alternative currency on bitcoin blockchain. See
http://counterparty.io/The real question is, however, why people would accept your alternative currency?
Depending on the miners' demographic distribution, it probably works in the same way as the original bitcoin issuance (hashing competition).
Launching a soft-fork-currency will stimulate the new mining competition, it is different from the random coin-creation on the Bitcoin blockchain. It creates scarcity because it will be directly backed by the world's biggest mining facilities (only one), and difficulty to make a soft-fork will ensure it will be done only in a really needed situation.
Miners also can promote the soft-fork-currency by giving some discount for their tx-inclusion service.