It's all a matter of money. Sure, it's technically possible to make a web interface to their ADR database, and make it user-friendly enough for the general public, and make it able to handle thousands of simultaneous users, instead of the relatively small group of CMs who use it now.
But, that's going to be a VERY significant expense, both for the initial development and the long-term maintenance of the system. And with very minimal financial return. If you spend several million dollars on a new ride or a new resort, you'll get a 'bump' in the number of visitors, as folks want to check out the new thing. Will more people go to WDW because they can make ADRs online? Highly unlikely.
I think that's a large part of the reason why Disney's computer systems are so antiquated. There's only so much money in the budget, and ride and resort development folks will get first crack at the money.
Companies spend money on development if they can 'sell' the result, or if they can save money due to cutting staff, or other efficiencies. Disney will only do this if they can lay off enough of the Disney Dining CMs to cover the cost of the system, and since they're probably getting minimum wage, the financial incentive will never be there.
Yes, it would be great for us to be able to book ADRs online. I'd love it. But, unless Disney can save money or make money by doing it, it won't happen anytime soon.