This number is only meant to be used by United Airlines' Premier Access members, so most customers won't get any benefit from calling it. When you do, you're asked to input your United mileage perks reward member number so the system can confirm your status as a Premier Access member.
Should you say that you don't know your member number or otherwise refuse to provide it, the system tells you it can't connect you with a Premier Access representative without that information, although it allows you to go through the automated system. However, once you've gone through that, you can't get any additional help without providing that number, and you must instead dial a different number to get any assistance with your issue.
Overall, I think having a number that's dedicated strictly to solving Premier Access members' concerns is a good thing. First, there's the fact that these customers are among the most loyal that United has, and anything the airline can do to help cut down on wait times for customer service concerns goes a long way toward making one-time customers into repeat customers.
Second, having a number dedicated only to customers who would be Premier Access members limits wait times among customers who fly regularly and thus know what to expect from United. During the busiest travel seasons, such as major holidays, many people fly for the first time in a while and perhaps only time all year. Having a dedicated line to get repeated travelers the help they need without a wait time makes a big difference in amplifying the customer experience for everyone.
The automated system also seems to be well set up, and I found it fairly easy to navigate the menu. There aren't many choices to make when choosing between current and completed travel, so there's a minimal wait time in getting through the menu and getting to the point where you need to enter your number to speak with a Premier Access representative.
Overall, I found this number to be well designed and useful for the advanced customers of United Airlines. The wait times for calling United aren't very long in my own experience, and having a dedicated number to help out experienced travelers drastically limits the chances of getting a long wait time or not being able to provide assistance with the issue. Based off the limited exposure I had to this number, I would certainly use it if I were a Premier Access customer in need of assistance.