Yes, services such as Uber from which someone can call for a ride and someone comes to pick them up for a reasonable price does cut down on the incidence of drunk drinking. Uber makes getting a ride quicker and more affordable than calling a cab. Furthermore, they made it cool for youth.
When people find or suspect that they are in a current state of intoxication, the easiest (and most responsible) thing to do is to call a friend or a cab. Uber provides both. It is basically a cab service with a more personable touch. It makes for an extremely convenient and quick option for those who may be less than in control of their own faculties, even faster and more convenient than a cab service.
Services like Uber cut down on drunk driving because it is a cheaper alternative to taxis and are more accessible too. A group of friends or an individual who plan to go out drinking would more than likely just Uber to and from the place where they are going to drink as opposed to driving their own vehicle. It makes it cheaper and easier to find a ride when you really want to cut loose.
Services like Uber or common taxis help cut the drunk driving because having another person or a designated driver to take you home after a party or a night out reduces the changes of someone under the effects of alcohol or other drugs, get a car and drive around risking his/her life and the life of others .