Washing Machine Drain direct to drain pipe vs laundry tub
Lint in drainwater should not clog pipes - it will just be carried along with the water. 

Whether it's bad for something further down the line (such as your septic field) will vary depending on things like whether there even is a septic field at the house in question, whether the tank has a filter before the drain field, etc. Generally not an issue if going into a public sewer. 

A laundry sink has uses, but is now uncommon as it also takes up extra space. In houses with limited drain capacity, the holding function of a laundry sink can take the high-speed washer output and let it into the drains more slowly without overflows. That's rarely a problem in "modern" house plumbing that's designed to a code which expects washer drains to accommodate typical washer output flows, but can be a big factor in keeping a laundry sink in an older house with less robust plumbing.