incorrect. whether the computation is 'useful' is an externality; it has no direct bearing on its suitability for use in bitcoin.
What about the integrity angle? I'm thinking along the lines that if the calculation does something useful (i.e. other than cryptographic security), there may be an underlying pattern to the result. If there is a pattern, then it can be reduced, and therefore attacked (someone figuring it out will be able to do a lot more of it than everyone else). This might of course be wonderful (figuring out shortcuts to problems improves general use), or not (attacker keeps it to themselves while abusing it).
bitcoin was designed to be entirely decentralised, and decentralisation has substantial costs. it may also have substantial benefits. time will tell.
It may not be realistic to expect Bitcoin to replace everything else, for those cases where the disadvantages outweigh the advantages it could coexist with other systems, perhaps even Bitcoin like ones with tweaked parameters.