It would theoretically work, but you would probably need dozens, maybe hundreds or even thousands of them to power a single lightbulb. They create almost zero power. They have barely enough energy to move themselves under their own power. There is almost nothing leftover to turn into useful work or electrical energy. As soon as you add the resistance of an electric coil, they will just stop, especially if even the merest hint of electrical load is placed on them, like you dropped them into a bucket of glue. If you don't think adding a mere coil of copper wire can stop such a movement, it absolutely would do so, instantly, like slamming on the brakes. As an experiment, try dropping a magnet down a copper pipe, or look at what this guy does. Moving magnetic fields (which are what you need to turn that motion into energy) are really wild and counterintuitive the way they instantly counteract their own movement into something resembling friction, but that turns into energy. Regenerative braking on vehicles does exactly this.
The problem with this kind of device is that its physical power output is so limited, even at scale, it would become a waste of physical space that would be far more productive, cost efficient, and reliable with wind turbines, solar panels, or even just batteries storing energy from some other renewable source.
There is no physical impossibility, it's just really, really, really, really impractical. It would be like trying to power your farm equipment by growing millions of potatoes to use as batteries for an electric tractor whose only purpose is to farm more potatoes. Okay, great thought, that's technically renewable energy, except you'd be better off farming something much more energy-dense and turning it into biodiesel or ethanol or something, and suddenly about 99% of the farmland you were going to use for battery-potatoes can now be used to grow actual food or cash crops, and you're still just as renewable and environmentally friendly so like... why would you want potato batteries, except just to say you can? Same with this idea. It's nearly impossible to get any useful amount of energy out of it. Yes it's "free" energy, and sure it's funny, but... nah.