Some large area rugs would look great, but I understand if you want to keep the housecleaning super simple.

It is easy for them to buy a rug if they really do want carpet. 

Should I put things like a new Rug, broken table and broken vacuum cleaner by tenant into depreciation ?

Because my girlfriend is, at this time, only owning a $5,000 share in the house, I as the homeowner have been solo paying for most of the many house-related things that a landlord/homeowner should: buying a refrigerator, window treatments, furnishings like rugs and carpets, shelves being installed, repairs etc.

The two main reasons I am here are to get an idea of the mindset and opinions of investors and landlords and to provide the viewpoint of the other side or the issue Which I think far too often get sort of swept under the rug if not flat out ignored. 

Cheaper way,  install higher end rugs that will match decor  and color schemes.It will help, not only on the floor noise but overall noise .As a contractor, if you do the sound board in ceiling below then just install it over the sheet rock and install a new layer of sheet rock. 

I had one tenant whose bathroom rug was covering missing tiles.

You're screwed, you need to whole new Drainfield. 3- There's a rug, boat, trailer, anything heavy or creating shade on the drainfield.

Needs cosmetic updates and new rug according to the pictures.

How does everyone handle noise complaints from the lower level of two-family houses if you've already asked the top level to put down area rugs?