My User Interaction Design friends don't agree with that assessment. The limiting factor in UI is not the computing power - it is limited by human perception and thinking, and that is not notably changing with the increase in computer power. The human mind only processes so much visual data at a time - so you always have a limit to how much you can present to a user, and thus have a minimum number of interactions to get into any particular activity.
Unless (and until) you are talking about direct neural input and interaction, the UI issue remains.
So what? Part of the nice things about newer technology is that we can make things simpler to use by abstracting more. With greater abstraction tends to come simpler design. Simpler design tends to increase usability. Greater usability generally means more information presented to the untrained user. The simplicity may bother power users, but y'know, I suspect even those IT folk who complain endlessly about the "dying of the command line" work in them less and less nowadays because there are fewer and fewer situations in which the command line interface speeds up their workflow sufficiently enough to bother with the difficulty of the interface. Sure, there's always "But I grepped the file and did a find/replace on every instance of <insert phrase>" types stories, but think about that.. that's a very extreme sort of deal. Most problems aren't that straightforward. Even then, modern GUIs can probably make it easier to more complex jobs than those, while still having similar response times to the user.
And that's not uncommon anywhere. Almost always, new features are difficult to implement because no one's figured out a useful means of abstracting that difficulty away, and as a result, tend to be harder to use for the user, because they have to know something of the design in order to use it. They're complex and tend to be hacked together because the people who built them are going to be interested in the fastest way of implementing that new feature, not necessarily the way that makes it simple to build down the road. That comes later. Once it becomes simple to build, that's when it becomes easy to use, because they can abstract things to another level to make things easier on the end user.
The first GUIs abstracted away the difficulty of commandlines, which were a way of abstracting away the complexities of the manual switches that themselves abstracted away problems of the punchcards that were the first computer interface found in the modern digital computer. I could go further, eventually to fingers and toes, but the point remains that each generation of interface has removed barriers to information transfer by abstracting away some of the problems of the prior generation. In each case, each new interface was, at first, hacked together, slow, and probably barely usable. But that was not the point. The point was that even in that state, they were simpler for the average person to use than the one that came before. So they became popular. But in order to build each one, computer power had to increase to a point that the next one became viable.
The newest interfaces are touch-screen and motion-based and speech interfaces; they are complex because of the way they interact with us, and require a lot of computation to be there in order for them to work efficiently. So they are comparatively new, and difficult to implement. But things are getting better. Touchscreens are getting more standardized, and thus easier to implement. They are becoming cheaper, so they are usable on more things. Videocams and Microphones are becoming a standard peripheral that no computer comes without, just as mice became once GUIs became popular.
That's how advances in technology make for better interfaces; by letting us sacrifice some of the advances in speed to focus on usability and to abstract away problems that existed before. Because we can abstract away some problems, we can choose to focus on others and lessen the amount of extraneous information needed to obtain that which really matters.
Ironically, D&D software's likely to head where MMOs, D&D's lineal descendants by way of the original CRPGs, already have, abstracting away the core mathematics in favor of presenting a simpler interface to the end user. The original CRPGs abstracted away mechanics more than D&D, so they became popular. Then MMOs abstracted away CRPG mechanics even more, and became popular. Then MMOs started abstracting away mechanics within themselves, and became still more popular. World of Warcraft has highly complex mechanics. But to the end user, the mechanics are pretty simple. Press a button, and you hit things, and if you drop it's health bar down to nothing before yours goes to nothing, you beat it. Occasionally, there are abilities that boost your health bar, or modify other statistics, but in general, you are good to go just knowing those few things. If you want more, you can look at the character sheet. You can look at statistics like your hit rate, your crit rate, how fast you hit, and how much health you have, among other things. But the great thing is, you can choose how complex you want your interface. There are some amazingly complex World of Warcraft interfaces out there. There are also some very, very simple ones. This is one reason World of Warcraft became popular. It abstracted away mechanics that were forced on the user in previous titles, and made the amount of abstraction involved a player choice. It made things simple. It is also probably simpler on the designers. Most of the items in WoW are quite standardized, with a number of systems that make things easier for the designers to focus on making the game fun, rather than on implementing any one thing.
And yet again, there is the reason computer software is going to come to D&D. We already play RPGs every time we play a computer game with a story. The designer's already crafted his tale, and we're simply playing through it. The reason D&D sticks around is because we want tales that we make, rather than those that are purely the GM's fantasy. But we don't want to make things harder on ourselves. That's why RPG players slowly find themselves moving more and more to video games. It's because they are simpler to play.
And yes, the mechanics will have to be almost totally in the background. That's the point. In order to compete with WoW, TV, or the internet, all of which have simplified things to the point that quite young children can use them with almost no training, those designing future editions of D&D have to make it possible to abstract away mechanical choices as much as possible and leave players to only those which are important. Like choosing to use X ability instead of Y ability, or choosing to use none at all. Gribble's and Canis's ideas for "power card-ization" of character sheets is not uncommon. WoW's Armory and character sheets work in exactly that way, and I presume EVE Online's skill builders and whatnot do things that way as well.
And for that, with modern screens, you can deliver the needed information on the screen in some amazingly tiny packages.