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"What about government supported fiat money implemented with blockchain?"

Not sure how that would supposedly work.

There is one interesting application of government, though: the distribution of the coins. That is what all the cryptocoins struggle with. A government could give every citizen an equal amount of coins, because they have a database of people.

"Is it really viable not to have safe exchanges?"

Some would say that they don't need exchanges, they want to be able to pay everything with Bitcoin. So they wouldn't need fiat money.

Apart from that, exchanges can be at least as safe as banks or traditional stock exchanges. I am mostly using one that is associated with a bank, in fact.