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As far as Electrum goes, from what I've read, I cannot trust the whole "your wallet can be spawned with a seed" setup. Im too paranoid with the idea that the right combination of words can spawn your entire wallet. It's a bit fucked up actually.
well your bitcoin core wallet is also an HD wallet meaning it is "spawning" all your keypairs from a seed, it just doesn't give you any mnemonic!
as for your paranoia, it all comes down to that random entropy the wallets are using. if it is good enough then the "combination of words" you see is showing that random entropy to you in a human readable form that you could write down.