> does the essential core of crypto boil down to having a public trust ledger?
A blockchain is a public trust ledger that is uncensorable because everyone who wants to can get both a copy of a random sampling of the messages pushed to it (by p2p node gossip of the txpool) and then also a copy of the canonical state (by p2p gossip of the chain-head; the ability of nodes to fetch previous blocks by content-hash; and the ability of all nodes to independently compute block validity and canonicity.) But this uncensorability means that blockchains must solve for the problem of DoS spam attacks, that would seek to fill the chain with noise messages, to the point that it bloats to an impractical-to-store size.
That's why blockchains [that have distributed posting authority, rather than being de-facto centralized "Proof of Authority" systems] always "have" (but not "are") some form of digital money built into them. The digital money is there to be what the old proposals for eliminating email spam called an "eStamp" — a cost for posting your signed messages/transactions that regular users can afford to pay, but spammers cannot.
Without the "eStamps", you just have an unworkable, ever-growing pool of spam noise.
If you choose to eliminate the noise by only keeping the messages that nodes care about store-and-forwarding (such that you lose messages when their originator goes offline, unless at least one other node has accessed them), then rather than a blockchain, you get a system like Freenet.
If you choose to eliminate the noise by combining store-and-forward with TTLs, with push-based probabilistic gossip, then you get the original Usenet numbers groups and SMTP anonymous remailers that presaged blockchains, and were invented by roughly the same group of people (the https://en.wikipedia.org/wiki/Cypherpunk s), being used to anonymously distribute PGP-signed and encrypted payloads in much the same way that blockchains are currently used to anonymously distribute transactions.
> Couldn't a bad actor repair a broken RAM chip with their own parts and it would still be officially signed?
No, because the point is that you get to know who sold them the RAM chips that went into the device, because the RAM chip vendor digitally signed the sale of those chips to them, and their repair job "consumes" that item in their own digital inventory to convert one manifest (representing all the parts in a phone with bad RAM) into another manifest (representing all the parts in a phone with good RAM.) The provenance of the replaced RAM chips "travels within" the provenance of the repaired phone. It's a tree of component sourcing, not just a log of repairs.