Can a CO make a company wear eye protection all day to prove a point?

As a unit, you are expected to look out for one another. Just because you have two eyes does not mean one is a backup. Plus, AR 385-10 in the Army, and OSHA 29 CFR 1910 Subpart I REQUIRE the wearing of eye protection where eyes can be injured. You should be looking out for one another. If I had been your commander, I would have done the same thing. But that should have already been caught and corrected. Apparently, your NCOs at squad and Platoon level dropped the ball, but you ALL are responsible for one another. That can get you killed in combat if you don't do that.

Yes. Yes. Yes
This is how a good unit trains.

And I bet, his point was made, and that everybody from that point on will not only wear eye protection but insure everyone else is wearing it as well. It's called peer pressure- if you are going to advance in the service you need to study pyscology

I'm working under the assumption that the OP meant "Should" instead of "Can" in his main title post.

We all know that Commanders have LOTS of latitude in what the CAN do. What they SHOULD do is much more Subjective in nature.

In this specific case, it sounds like one soldier was acting like a child, so the CO is treating EVERY soldier like children.

Is that correct? My personal opinion is no, at least not with this very specific "Object Lesson." That doesn't mean there aren't better unit wide Object Lessons that would apply directly to this case. Like having a unit wide safety standdown where everyone has to sit through 3 of the most boring hours of power point presentations to the point where they WANT to stab their own eyes out with a fork, followed by instruction on the proper wear and maintenance of eyepro, followed by an "all day exercise" where everyone is wearing eyepro throughout the unit area (duplicating the above).

Eye-Pro - part of the modern protection gear.
Friend of mine lost an eye when a double feed cooked off in 1976 - Could a set have saved his eye?
I don't know but I do know in 2013 my face was sandblasted from a near miss and have no doubt they saved my sight from chunks of rock embedded under the skin of my face.
I met a Soldier who lost his eye to walking into a stick-end while rushing forward - No Eye-Pro and now no left eye.
You and your unit's NCOs should hang their heads - you failed in your duty, further its a crying shame that the CO had to fix the problem.

Some CO go overboard I don’t think mass punishment was the correct answer

Uhhh, were you even in the military? Damned straight they can. I'd like to have a nickle for every time we ALL paid for the infraction of one. it's called cohesive discipline.

It's called teamwork and the Team needs to look out after each other because often the mistake of one can really wreck the team.

Yes the punishment was for a good reason you need to wear eye protection because you never know what will happen. I have had to wear eye patches because I was welding and the person 50 yards behind me was welding also ,ended up with flashburns from the reflected flash . Wore those eye patches for three days was told I was lucky I didn’t lose my sight

This reminded me when our 1SG helped one of our young SP4s learn how to fasten his chin strap during road convoys... Back in 1985 with the 7ID(Light), we were redeploying back to Ft Ord from Ft Hunter Liggett with our jeeps (just before HUMVEE days) after a 3 week FTX. The standing order was to fasten chin straps as a safety measure on this 100 mile trip. Fast forward.. back in garrison..driving back from lunch and I see SP4 Patterson mowing the company lawn wearing LBE and his Kevlar helmet with fastened chinstrap. Apparently, Patterson did not comply with this safety measure and Top found out. Once inside the company building, I asked 1SG Terlaje about Patterson's lawn mowing attire.. Top said Patterson was engaged in training on how to wear a properly worn Kevlar helmet. Roger that!!