I defer to your understanding of Locke; you've drawn a very clear distinction between government by consent and government that protects unalienable rights regardless of consent. I wish you were around when I tried to discuss social contract on my Lysander Spooner threads.
As to the consept itself, I believe it to be self-contradictory unless unaleanable rights are understood, as I understand them, as something that can be consented away. Your description already produced a government that would consider suicide illegitimate, -- hardly a government rooted in liberty. More relevant to the issue of good government is the unalienability of property rights. In that arena, trade by its very essence is about consenting rights away: I abandon my rights to a dollar, you abandon your rights to a hamburger. Thus if property rights can be consented away, then we have a foundation for a state that taxes you at 50% (or 99%) of your worth. If property rights cannot be consented away, we don't have property.
I believe that the proper philosophy of rights is to distinguish between rights that are granted by authority (e.g. a right of way across property or a right to vote) and rights that do not require authority (e.g right of self-defense, non-disruptive speech or property). The latter are natural or unalienable rights; but either can be contracted, i.e. consented, away. The government derives its legitimacy from the consent of the constituents to the future laws that the present lawmaking process will produce.
If you'll forgive my saying so, you've got it exactly wrong. An inalienable right is one that can't be consented away; that's the definition of "inalianable". Your understanding is the self-contradictory, you're saying that something can only be inalienable if it can be alienated. You may disagree that there are inalienable rights, but you can't take them to be alienable.
Your description already produced a government that would consider suicide illegitimate, -- hardly a government rooted in liberty.
It's not clear what Locke would've thought. His argument against suicide was the same as his argument against murder, that both you and others belong to God, and as such should live on the Earth as long as He pleases, with just punishment for crime the only reason a person could rightly kill someone. He cited the commandment to Noah after the flood, "Whoso sheddeth man's blood, by man shall his blood be shed," to show that his one reason for killing someone was authorized by God, and therefore didn't contradict his argument from God's ownership. What I don't know is whether or not Locke regarded suicide as a crime in the Earthly sense.