The Pitch (slope) really has little bearing on basin waste UNLESS the waste for some strange reason doesn't go vertically down right after the trap
Very few sink wastes do go horizontal and even then only for a limited distence
On tub or shower YES as they are lower so pitch is much more critical
Water seeks its own level as the trap can be as high as 16" off the finished floor so the piping would have to actually face up hill in order to cause a sink to over flow
Normally other fixtures are connected to a basin waste thus utilizing the shower or bath tub waste arm also
The possible problem is the idiots out there installing wastes are looking for the cheapest get in and get out approach and cut as many corners as they legally can get away with
For example some lax plumbing codes do allow for 11/2 and some even allow 11/4 waste for a basin, to compound this under sizing of a waste line they use very short radius fittings such as a PVC 90 deg bend
If the installer was looking for a long term relationship with the account they would have used a 2" x 11/2" Sanitary Tee for the drainage and at least an 11/2" vent
What a highly skilled caring plumber would consider is explaining to the victims of an alterations the choice of materials available
There is nothing wrong with plastic piping for vent or even waste if installed properly but a much better choice would have been no hub cast iron with a long radius fitting such as a sweep which allows for a much better flow and easier to snake or water jet the waste line and it is a quiet system
The correct way to test a fixture is to place a stopper in the drain, fill up the sink to the over flow, then release the stopper and time how long it takes to actually drain
A basin is considered 1 fixture unit which is 7.48 gallons (1 cu ft) and a basin should drain from filled to totally empty in one minute or less
Also many so called plumbers will snake a line, a few month later it blocks up again and monkey see monkey do another ape minded person will snake the same line not thinking outside the box
If snaking is not providing a long term relief from stoppages then why continue doing the same useless task?
Over time the internal diameter of the piping decreases like harding of the arteries.
Snaking is great for removing hard stoppages rags, hair etc. water jetting is used to scour lines to restore full flow as originally designed by removing scale, soap scum deposits, oils that adhere to the internal piping that snaking will just bore a small holes through these deposits