My TV remote died due to battery corrosion  

What pisses me off is that inevitably the cover for the battery compartment breaks and you have to put tape over it.

Game controllers use bluetooth, TV remotes use infrared. Bluetooth is radio waves, it can go a limited distance, but can go through some obstacles. IR needs line of sight.

Howver, IR uses way less power than bluetooth, can go a longer distance and the line-of-sight requirement can be a good thing. For example, if you have multiple TVs in different rooms (or even the same room) made by the same manufacturer. Yes, you could pair the remote with the TV, but that would create a new problem - you wouldn't be able to use the same remote on different TVs.

I have two AC units, both are made by the same manufacturer, so both respond to the same remote. However, while the remote is IR, the sensitivity is ridiculous - I can be pointing the remote away from the AC and it would still respond. Most of the time I only use one of the units, keeping the other off by turning off the circuit braker. Sometimes I need both of them on. When both are on it is really had to adjust only one of them without having the other one react. I need to put my hand on a specific spot on the unit I do not want to react (yeah, I need to cover the IR sensor, but it is not visible from outside, so usually it's just trial and error).

My LG plasma TV has a remote that works using radio waves (I think) and while I can use it while it's still in my pocket, it drains the batteries much faster than the IR remotes.