pianotuna, are you Canadian? I don't know about intestacy there, but the OP is in the U.S.
There are no states that provide that the government takes anything by virtue of a person dying intestate. Every state has an intestacy statute that lists who inherits property in the absence of a valid will, and none of them include the government as a beneficiary.
If a person who dies intestate has no family whatsoever (including distant relatives) who can inherit the estate, then the estate escheats to the government, but the government is not a beneficiary; it is just where the property goes because it has to go somewhere. This obviously almost never happens.
If a person has family members and dies without a will, the government will not get the estate. It may not be divided up among the family members the way the dead person may have wanted, but it will go to family and not the government.
I do wonder, since your wording has changed a little bit, to "by the time the government is through," if you mean that an intestate estate might be reduced by costs of administering it. That's entirely possible, since a court will have to determine who the family members are. That will involve a lot more work than merely probating a will, but it is not the same as the government "getting" someone's estate if they die intestate.
Also, note that states have different requirements for holographic wills. One that is hand-written and includes a witness' signature still might not qualify as a will and will have no effect whatsoever--it will be as if it didn't exist at all.
Living trusts can be a good idea in some states, but note that all of a person's assets have to re-titled to be owned by the trust. It's not hard, but if you forget an asset, or buy something without thinking to put ownership in the trust, it won't be covered by the trust. For that reason, living trusts (should) always also have a will, just in case something gets left out. And it will have to be probated if there end up being assets that aren't owned by the living trust.
