I don't know if you are old enough to remember it, but that's exactly what nuclear energy proponents said in the 70s.
Since then, actual experience showed that about every 20 years, there has been a big incident with global impact, and it will take decades if not centuries until the affected area is usable again. And the latter is something that might be tolerable in less densely populated countries or locations (Chernobyl), but in very densely populated ones it would be a major catastrophe.
And so far we've only seen disaster scenarios caused by human error and force of nature, and there's a third one (human malice), which thankfully hasn't happened yet, but which is impossible to guard against.
So my conclusion from reality is that no, we can't make nuclear power completely safe: The consequences of a disaster are too great, the monetary incentives are all wrong (it's not the nuclear companies which pay in case of the disaster, the state takes over; and the costs of the risk are not factored in into the actual running costs; and safety measures are expensive, so economics will always lead to, say, putting the backup generators NOT on the hill, because that would have cost more).
And then there's the problem that in some countries using nuclear energy and producing nuclear waste, the problem of actually storing that waste safely for the next few centuries is still not solved. Even after 50 years of producing it. And that is just insane.
I wish we could make nuclear safe. It would be a great way to reduce carbon emissions. Looking at reality, I can only conclude that we can't, and it's wishful thinking. (Yes, I know, that opinion is not popular, and the nuclear fanboys will be all over me, but so be it).