Well, it would derpive Britain of her single naval base in the Blakc Sea. Might still be better for the UK in the end, though, given how much argument and strife with Russia and the Ottoman Empire this has caused, the one wanting the city back, and the other always bitching about Bosporus passage rights. Who knows, maybe with less British ressoruces going there, GB could have played a more active role in other parts of the world, like, say, Africa - for it being th enaval power of the tim eit got majorly underrepresented in the Ramble for Africa!
And I guess no Second Crimean War would have helped state finances, too. Might even be that without teh Second Crimean War occupying the attention of two Great Powers German unification wouldnt have happened, at least not in the 1860s. So, yes, IMO, Sebastopol only gave a large burden to the GB, at least up until the 1950s, when it became the booming tradecentre we know it as nowadays.