They wouldn't. That's why passengers aren't tasked with being safety inspectors.
Are they on the ramp waiting to get ingested into an engine?
Are they jammed in the flap tracks?
Are they embedded into the leading edge of tail surface after flying off in flight at cruise speed?
Its one thing to say that you can fly without those screws on the MEL. Its a whole other thing for parts to be falling off of an airplane in operation, even if they aren't required.
A single piece of metal that fell off of a different airplane is what caused Concorde to crash.
A non-required screw that backs itself off and falls off in flight is a maintenance procedures failure (torque or locking compound was ignored). Screws don’t just fall off. Ignoring it because it is non-required is dangerous because it could possibly indicate that screws are being installed incorrectly, including required ones.
Qualified mechanics certify every single non-experimental plane as safe. Yet somehow, planes still crash for mechanical reasons.
What kind of risk are we talking about? When did that last happen on a commercial airliner? How many people have been injured that I should be 'very concerned'?
It’s a big enough issue that every airport is required to have a debris management program, and runways and taxiways are regularly swept by specialized equipment.
FOD is estimated to be a multibillion dollar problem by more than one study.
If I was going to be 'very concerned' about potential risks without considering mitigation, there's fuel tanks exploding, running out of fuel, drunk pilots, hitting mountains, runway collisions, etc. etc. Pieces of FOD don't seem to rate ...
My point is about risk, of course. FOD is not an effective risk to me.
Concorde had decades of documented tyre problems. That was a flawed design (tyre and fuel tank) that allowed this crazy outcome.
It was a strip of metal that had fallen off of another airplane a few minutes before.
Concorde did have a higher risk due to its higher takeoff speed, but the only fatal accident in the airframes history was directly caused by a piece of metal that fell off a different plane.
There's an engineered threshold at which an aircraft is deemed not airworthy. On airliners, this is managed through a Minimum Equipment List (MEL), which is a formal checklist that tells the crew which equipment is allowed to be broken (and for how long).
This threshold is less than 100% by design, because little things break all the time. It can take days/weeks in the shop to fix issues, so you need to batch up all the maintenance. (Can you imagine if you had to take every aircraft offline for several days after every flight?) And that's okay, because there's still a large safety margin built in as long as the MEL is followed.
That's exactly what the air force does. Most of their jets require tens of hours of maintenance for every flight hour!
Who has done that? One plane lost a plug, with no injuries. Who else has gotten even injured in a commercial US flight in the last year?
Some of them matter, and the pilots keep a close eye on those during the preflight checks. Others, matter less so. (A single missing screw on a prop spinner - big problem. A missing screw on a non-structural plastic aerodynamic fairing - okay to defer, literally zero risk.)