How hard would it be to successfully attack (all) the Electrum backend servers? I think there is about a handful of them.
I would consider an attack successful that stops Electrum from working for a day or so.
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I'm not exactly sure if this is what you're asking; nevertheless the wiki says:
Transactions are signed locally: Your private keys are not shared with the server. You do not have to trust the server with your money.
Freedom and Privacy: The server does not store user accounts. You are not tied to a particular server, and the server does not need to know you.
It seems the storage of your keys is client-side, so if they were to get (D)DoS'd you could easily move you keys to another wallet.