Bridge and dam design, passenger aircraft and spacecraft design and nuclear reactor design require absolute avoidance of catastrophic failures or the loss of public confidence due to obvious oversights and professional stupidity.
This is impossible. It will never be safe. The planet we live on is not safe. We could all get hit by an asteroid, obliterating all of us. To survive this type of events, nuclear plants would need a mile thick concrete wall. It'd be a pretty pointless investment, since all humans are dead, no one will care about the intact nuclear powerplant.
Passenger aircraft are not safe. Many people die every year by aircraft crashes. No one has died in the last year due to radiation from nuclear powerplants anywhere in the world.
Bridges and dams are not safe. They sometimes collapse. Even recently this has been the case. Dams are inherently unsafe because you're pitting yourself against gravity with lots of unknowns in hydro-geology - the exact state of all rock layers can never be 100% ascertained - and all you've got against it is engineered layers. It's physics against engineering. It is even more the case with aircraft - hugely complicated engineering and electronics versus gravity. Gravity will always win when things get tricky.
Cars are also inherently unsafe, with incompetent idiots driving behind the wheel, the human factor squared. Unsurprisingly, traffic accidents kill 1.2 million people every year, 300 Chernobyls a year. It would be sane to spend more to make cars safer, rather than wasting this money on nuclear plant safety (no one builds Chernobyls anymore, the worst you can get is a Fukushima type, loss of all cooling, which kills no one).
Aircraft and bridges/dams are built to reasonable standards of quality control and assurance. Nuclear plants must be built to unreasonable standards of quality control, costing billions per plant, even though an historic analysis of nuclear meltdowns shows very little to no influence on quality control.
Once you realize safe is a relative term, we can further the discussion. It is relatively very unsafe to design a nuclearpowerplant to require electricity for cooling and then situate it in an area that regularly gets large tsunamis of 10-30 meters tall, with only a few meters design basis tsunami defence. It is relatively very safe to not bother about dinosaur-obliterating asteroid impacts in the design of a nuclear powerplant. Somewhere in the middle we are going to have important discussions and will have to draw arbitrary lines of what we find acceptable and what not.
It is clever to design nuclear powerplants with elimination of failure modes, where this is impossible, make the failure fail-safe or at least as benign as you can. It simplifies the discussion of remaining failure modes.