Prolonged and Significant Lithium Shortage
On reason we've been able to increasingly make a large number of items be wireless does sort of rely on our current level of battery technology - this is partially inspired by @tjlaboss's answer about how the reason things are wired is that they're power cables, and working to figure out what would require battery tech to not be able to withstand the output of our devices.
There are a few different types of batteries, but when focusing on rechargeable batteries, there's an easy way to note why Lithium-ion based batteries are significantly used today:
1.) They have a higher capacity than Nickel-Metal Hydride (NiMH) and Nickel-Cadmium (NiCad), or even Nickel-Zinc (NiZn).
2.) They discharge at even 3% less per month than the next best option, NiZn batteries.
3.) They have high voltage outputs, so you don't need to chain 4 or more* batteries in series just to power a device at a time.
1.) helps deal with the discharge in 2.), and both of them are affected by 3.).
So getting rid of lithium batteries would put a strain on the use of wireless devices. If lithium batteries are removed and the next best options are used - it's likely smartphones/cellphones and wireless headphones would be strongly incentivized back to wired connections to save on the need to actually have and replace AA or AAA batteries every so often*. And the easiest component to put a stranglehold on is lithium itself - while it can be used in semiconductors as well, although those have alternatives as well that work, such as silicon, germanium, and gallium arsenide.
How you get there could be a matter of labor shortages in the mining process, or a reduction in available lithium in the world, or large amounts of fiery accidents that cause us to go through it quicker without being used in wireless products properly, thus reducing the output of lithium batteries.
That said, it'll need to be a significant amount of a lithium shortage to really make this change a permanent effect in the future - we apparently had a 9-12% supply deficit in 2021-2022, and people are still able to get access to lithium batteries for manufacturing purposes.
*Based on the math some people made here, it varies how many batteries you may need to charge a phone with AA batteries - anywhere from 3 to 13 batteries, depending on how much you need to charge a phone. With a rough estimate here indicating that you would need to have 2 batteries being charged 1000 times to keep the phone charged for a year. That amount of work to keep a wireless device wireless will likely lead to people increasingly going for wired AC power powered devices where possible.