I did have the battery problem... eight years ago, when the battery in my then not-exactly-brand-new mouse started to lose charge much too fast (I had a Logitech Cordless Desktop MX, which later got released in a Bluetooth version rather than the proprietary version I had). I don't know exactly when the combo was released, or when I bought it, but the manual for the mouse says copyright 2002, so it's been well over a decade and battery and energy saving technologies have both come a long way since then.

It is possible that my experience is coming from older products and from worse manufacturers.
Probably newer technologies are better and some manufacturer make better products than others.

So it is possible if somebody buys wireless keyboard+mouse combo he won't experience the first two disadvantages.
But I don't think anything could fix the input lag. But many players won't notice that. Only those who plays CS:GO around global elite rank for example.

I guess there is some (theoretical, at least) lag compared to wired, but at least I haven't noticed it when playing e.g. TeamFortress 2 online (Casual or Competitive, doesn't really matter). It is the other things that may annoy more, like that a wireless mouse tends to be bulkier and heavier than a wired mouse (due to the battery inside), which does affect the gameplay experience somewhat.

If wireless lag was an universal issue, wouldn't console players be pretty much screwed as the controllers of new consoles seem to be only of wireless variety nowadays? They still play high-speed action games with them too, like fighting games and such. If there was noticeable lag there, they'd be constantly complaining.

I dont want to be rude but I don't think most of the console players are serious competitive gamers. They don't really care about these microlags probably they don't even notice it. Comfort is more important for console buyers, so companies are selling it with wireless contollers. And if somebody wants he can buy a wired one but it is not the majority of the customers.

Most of the multiplayer console games have worse netcode than PC games.
For example Overwatch came to consoles and PC with the same netcode. But after the criticism they changed the PC netcode relatively fast. The console netcode is still the same.

About the fighting games, serious players are buying fightsticks and not playing with contollers.

And as I see on console Esport events, players are using wired controllers not wireless ones.

There is a lag but you will notice only if you play on high level.
If you are not, you can even play with a wheel:
https://www.youtube.com/watch?v=Fl35QCbMi-c

Edit: And I didnt mention the 30fps limit on many console games. There are so many thing causes lag, u wont notice one more or less.