It is almost always implied. It seems so obvious that nuclear should be replacing fossil fuels it doesn't seem worth mentioning. Unless someone says they're aiming for an energy policy of nuclear plus fossil fuels, it's probably safe to say their goal is nuclear and solar/wind/etc.
Even the volcano comment you mention ends with "For energy we obviously need all the options available."
No, it wouldn't. Batteries + renewables is proven and it works. The problem isn't a technological barrier. The problem is we need batteries for a lot of things and production can't ramp up fast enough.
Technical barriers are always also resource availability barriers, since technics also condition both usage and availability.
People picked tribes and decided it's all or nothing. I agree--that's stupid. There is a historical alignment between renewables backers and anti-nuke activists (see: Germany) that caused nuclear to polarise away from renewables. That doesn't really exist anymore. But you see its artefacts in the debate.
Even in this thread someone is saying that the problem with solar is that "if a megavolcano darkens the atmosphere... thus we should go all in to nuclear", as if it was a guaranteed event in the next 100 years.