Someone already referenced the difficulty present for those who do not wish to be independent.
People who do not like things can leave, and find a country where they do like things. However, changing your national status forces this change upon people.
Additionally, for many countries there is an entitlement concern.
Crimea for example, imports approximately 80% of its electricity and water from the Ukraine. It has no overland routes to Russia (a bridge will take time and billions of dollars). The Ukraine did not want Crimea to take this vote, and by rights could now close their border and shut down all water and electricity exports, or charge exorbitant prices. In reality they wont do this. But Crimea has essentially demanded independence, whilst continuing to demand social and financial support - which is of course ridiculous.
That is a common problem with independence declarations. Though far more complex, there is a similar complication in Gaza.
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