That would mean, that the initial Proof of Work is the only thing, protecting the whole system. Because then, someone could make a different alternative chain, where initial Proof of Work will be bigger than previously, and then effortlessly make any signatures on top of that. Which means, that the whole consensus would be again "obscured Proof of Work", where instead of targetting current signatures, attackers could target the initial Proof of Work, before the switch to staking. And if you make the initial Proof of Work impossible to overwrite by consensus rules, then it doesn't matter, if it will be there or not. Then, it will be just a full Proof of Stake, and it doesn't really matter that much, how you will pick initial owners, if "51% once, 51% forever" will still be true after transition to signature-based system. Of course, instead of having 51% coins, your consensus could assume 51% cosigners, but it will only make things easier to attack, than existing Proof of Stake systems. Not only that: it doesn't have any upper value. It is not limited by any consensus rules, so people can endlessly make new UTXOs. And in your consensus, there are no protections from making more outputs than needed, just to increase chances of being selected. In existing chains? Yes. But in your consensus, there is no incentive to do that, if they can sign more things by owning more UTXOs. Quite the opposite: everyone has an incentive to make UTXO set explode, and produce more UTXOs, than everyone else.
That would mean, that the initial Proof of Work is the only thing, protecting the whole system. Because then, someone could make a different alternative chain, where initial Proof of Work will be bigger than previously, and then effortlessly make any signatures on top of that. Which means, that the whole consensus would be again "obscured Proof of Work", where instead of targetting current signatures, attackers could target the initial Proof of Work, before the switch to staking. And if you make the initial Proof of Work impossible to overwrite by consensus rules, then it doesn't matter, if it will be there or not. Then, it will be just a full Proof of Stake, and it doesn't really matter that much, how you will pick initial owners, if "51% once, 51% forever" will still be true after transition to signature-based system. Of course, instead of having 51% coins, your consensus could assume 51% cosigners, but it will only make things easier to attack, than existing Proof of Stake systems. Not only that: it doesn't have any upper value. It is not limited by any consensus rules, so people can endlessly make new UTXOs. And in your consensus, there are no protections from making more outputs than needed, just to increase chances of being selected. In existing chains? Yes. But in your consensus, there is no incentive to do that, if they can sign more things by owning more UTXOs. Quite the opposite: everyone has an incentive to make UTXO set explode, and produce more UTXOs, than everyone else.

That would mean, that the initial Proof of Work is the only thing, protecting the whole system. Because then, someone could make a different alternative chain, where initial Proof of Work will be bigger than previously, and then effortlessly make any signatures on top of that. Which means, that the whole consensus would be again "obscured Proof of Work", where instead of targetting current signatures, attackers could target the initial Proof of Work, before the switch to staking. And if you make the initial Proof of Work impossible to overwrite by consensus rules, then it doesn't matter, if it will be there or not. Then, it will be just a full Proof of Stake, and it doesn't really matter that much, how you will pick initial owners, if "51% once, 51% forever" will still be true after transition to signature-based system. Of course, instead of having 51% coins, your consensus could assume 51% cosigners, but it will only make things easier to attack, than existing Proof of Stake systems. Not only that: it doesn't have any upper value. It is not limited by any consensus rules, so people can endlessly make new UTXOs. And in your consensus, there are no protections from making more outputs than needed, just to increase chances of being selected. In existing chains? Yes. But in your consensus, there is no incentive to do that, if they can sign more things by owning more UTXOs. Quite the opposite: everyone has an incentive to make UTXO set explode, and produce more UTXOs, than everyone else.

That would mean, that the initial Proof of Work is the only thing, protecting the whole system. Because then, someone could make a different alternative chain, where initial Proof of Work will be bigger than previously, and then effortlessly make any signatures on top of that. Which means, that the whole consensus would be again "obscured Proof of Work", where instead of targetting current signatures, attackers could target the initial Proof of Work, before the switch to staking. And if you make the initial Proof of Work impossible to overwrite by consensus rules, then it doesn't matter, if it will be there or not. Then, it will be just a full Proof of Stake, and it doesn't really matter that much, how you will pick initial owners, if "51% once, 51% forever" will still be true after transition to signature-based system. Of course, instead of having 51% coins, your consensus could assume 51% cosigners, but it will only make things easier to attack, than existing Proof of Stake systems. Not only that: it doesn't have any upper value. It is not limited by any consensus rules, so people can endlessly make new UTXOs. And in your consensus, there are no protections from making more outputs than needed, just to increase chances of being selected. In existing chains? Yes. But in your consensus, there is no incentive to do that, if they can sign more things by owning more UTXOs. Quite the opposite: everyone has an incentive to make UTXO set explode, and produce more UTXOs, than everyone else.