Some alterna-coins may not rely on the same sort of processing power as Bitcoin. For example, Bitcoin mining has migrated to specialized GPUs and ASICs. Litecoin specifically chose 'scrypt' memory-hard hashing, for which the same GPUs/ASICs provide no benefit. Other 'proof-of-stake' proposals for maintaining the ledger emphasize staying actively connected to the network – pulling your own weight in verification and distribution – rather than raw hashing power.
Bitcoin's proof-of-work-during-verification trick is neat, but may not be the only way, and thus viable alternatives may emerge that don't face the barrier of an early miner decision to redeploy computational power elsewhere.
In the proof-of-stake proposals, actually holding old balances, and actively helping to certify transactions when challenged to do so, is what earns you the right to 'mint' new ledger-extensions. (And if you don't, your future transaction fees go up.)
Not sure all the kinks are worked out, but competing based on who best enables the fastest, most consistent, most-fraud-resistant global log seems to more directly benefit the community, than proving who's burned the most resources on electricity and specialized hardware.
Bitcoin's proof-of-work-during-verification trick is neat, but may not be the only way, and thus viable alternatives may emerge that don't face the barrier of an early miner decision to redeploy computational power elsewhere.