This part is taken care of by 3rd party companies so I can only half answer that. It bring zero savings to the hotel other than a insignificant amount less garbage that is taken away.

Recycling like this is much better and easier because you have large quantities of the same types of plastic all together. This makes processing, sorting and recycling easier. The soap itself is easy to process

Hey I actually helped create this program. And as info the soap is given to third party companies, plastic is recycled (if bottled soap / shampoo), then it is hygienically processed and donated to a variety of causes. Let me know if you have any questions, but it's not (for once) horrible capitalism something or reused in the hotels.