Its not trust as trust between humans - it is just anti-DDOS between machines using the same hashing that Bitcoin uses same as hash cash etc. etc. etc..
You can call it what you like but it's a persistent identity which can be targeted for abuse. If an attacker wants they can farm them and have an advantage against honest users, potentially an avenue for coercion and theft, etc.
I'm calling it what it is DDOS protection.
Please do explain how you plan to steal from or coerce a randomly generated key with 2 minutes of hashing work behind it.
I'll wait.
The scheme you've described is largely incompatible with pruning too, since to validate nodes randomly need historic data that today full nodes don't even need to retain.
Why?
Nothing prevents nodes from removing TXs with spent outputs in their chunk range although it would require some polling/notifications.
Not that it matters either way because these swarm nodes would cost 1.6 $ a year in HD space...
If it's sufficiently minor then it provides little protection. In either case it's a concrete cost against running a node.
A concrete cost of 2-10 minutes of CPU? Are you being serious right now?
Even a small thing like that would make spam attacks difficult.
That it also make it possible to verify blocks fractionally (at your random choice) without having to trust data from third parties is what I was mostly referring to...
How do you verify no double spends "randomly at your choice"? You need the complete history to do that (minus some swarm design ala mine).
I don't see how a minor change in signature storage changes that.