I have a deal with all of the animals. They stay out of our houses, we leave them alone. We can't coexist in a home with wild rodents for sanitary reasons. Thankfully, at my home only ants don't get the memo and must be poisoned at scale outside their favorite point of access.

(Spiders have a special deal: Just stay out of sight while inside and we're gucci. But I'll just move them outside because I see them as allies against the insects.)

Because I do not want hantavirus. Their droppings spread nasty diseases.

If you poison them then they die in the walls or somewhere you can't get to them and stink. Shooting is the sporting method (a very low powered .177 air pistol works well indoors if you take careful shots), but trapping also works. You can make a trap guaranteed to kill a rodent with a sheetrock bucket, a butter knife, and a delicious morsel. Walking the plank is a much more effective method of execution than the spring loaded guillotine, no partial results.

Mice are cute as hell, but we have traps on the kitchen counters (they come in in the fall) because they shit everywhere they walk. It's not as clear-cut as you make it out to be.

Sanitation and disease prevention. Traps are probably better though.

Plauge.