There are three main reasons why Disney will not check the tickets over the phone, none of which has anything to do with their ability to find out what's left on the tickets. In no particular order of importance, they are:
1) To impede the illegal resale of partially used tickets.
2) To avoid the guest misreading the numbers on the ticket (which happens often when an 3 gets misread as an eight or a 6 gets misread as a zero, etc) and then being given the incorrect information about the ticket. That eliminates unhappy guests screaming at a Guest Relations CM at the parks when the ticket is swiped and the guest finds out that what's left on the ticket isn't what they were told on the phone.
3) Staffing issues. You want to check your three or four tickets to see what's left. Now multiply that by the (hundreds of) thousands of other people in your same situation. Then add in the people buying/selling on Ebay and other places who want to verify what they are buying/selling. There wouldn't be enough hours in the day for the ticket research people to handle the volume of calls that they would get.