But it's at least possible, from the protocol, to determine the balance of each address, and for each address to vote (with a message on the blockchain) for or against a given proposal.
Compare that to trying to determine which address "probably holds more influence", which seems like something you'd have to trust someone else's (off-chain) judgement on.
As in software, a lack of determinism means a lack of reproducibility, and without reproducibility it's harder to have consensus.
In particular, if bitcoin makes a rule change (or refuses to implement a rule change), such a decision lacks the transparency and accountability needed for good governance, because the bad actor can just say "Well, that's just how things worked out that time. Blame the RNG.".
I don't think this is a theoretical concern when it comes to a bad actor corrupting the bitcoin protocol development process.
It's related, yes. The main difference is that rather than your power being determined by how much bitcoins you hold, your power is determined by how much influence/power/contribution you have in the overall bitcoin ecososytem. A major merchant might not hold that many coins compared to the average whale, but probably holds more influence.
>so they require even more trust.
I wouldn't say it requires more trust. It's not like bitcoin holds an election every few years for determining which party holds the economic majority.