Imma answer this sorta seriously:

When you wipe like you're attempting to scrub away a particularly peculiar protruding posterior particulate you are often actually just causing damage to the rather soft and sensitive rectal tissue. This typically results in irritation. This irritation can lead to itching. Itching leads to the need to scratch, which can take the form of wiping.

Thankfully (usually) the body tends to focus a bit more on areas where bacteria frequent. So abrasions or tears in the rectum won't normally cause further complications. However, it is recommended to seek relief from symptoms by obtaining a safe anti-itch cream, being gentler, and generally just coping. I suspect that a bidet is also recommended because it causes less/no trauma to an area already sensitive, especially when healing.

For burning, such as from spicy foods, I'd guess a bidet acts in a similar fashion to running a minor burn under water until the pain subsides. Just don't go shoving any sterile gauze up in there unless you want to be featured on one of the Fire Department Chronicles' shorts.