> Why not?

Because weekly pickup is expensive to run.

In most places you pay for your weekly pickup one way or another. There’s no way people are going to vote for or approve an additional weekly pickup charge for something they dispose of very infrequently.

There are many stores with battery drop offs. If you really want to make a dent, put the battery recycling drop offs in grocery stores and put signage around it.

Routine pickup would be more hassle: You’d need to figure out the bins, the pickup method, the scheduling, etc. It’s really terrible for anything that isn’t both large and steady, like your waste bin.