What do we mean by "dialect"?
First of all, let me say that the distinction between "dialect", "slang", and "language" is fuzzy, arbitrary, and fundamentally a social (cultural, political) construct.
Two dialects of the same language can be mutually unintelligible (e.g. Moroccan and Baghdadi Arabic — significantly different on every level), while two separate languages can be almost 100% understandable (e.g. Serbian and Croatian — considered different for nationalistic reasons by some). You can also have a language continuum; for example, Dutch and German are completely different languages. If you start out in northern Germany, and start heading (along the correct path) from town to town, you'll find that each neighboring town understands each other, but once you are in the middle of the Netherlands, you'll realize that people are now speaking dialects of Dutch, and at some point you crossed over from one to another, but there was never a line where one group is speaking German and the other speaks Dutch.
Defining what a "language" is in real terms
A good way to think about why we have dialects and accents is if you don't think about a language as a single entity of some kind. Each official "language" is more of an abstract concept. Instead, you can think of language as a distributed system, where no member of the system (any speaker of the language) has complete knowledge of the system. Those members who come in contact with each other influence each other as they communicate and interact, meaning that there is bi-directional feedback between members. Due to things like innovation, misunderstandings, reanalysis, and borrowing, random elements enter into the system and drive change. Also, the population is always adding new members who are more malleable and losing older members.
The more isolated and coherent a group of people are, the more these types of variation lead to deviation in the form of the language, because the repeated interaction with members having similar grammar leads to a sort of feedback loop. (You can think of this as being somewhat analogous to isolated groups of people having genetic defects or features in common, because the repeated combining of similar DNA amplifies subtle mutations.)
This is happening all at the same time, with "group of people" being defined at all levels, and all updating and influencing each other at the same time. For example, each person has his own way of speaking, and households will often develop unique features in the way they speak. Different age groups, genders, and other culturally defined groups may have their own features as well. People's grammars are being influenced by their peers and, in turn, influencing their peers.
Looking at language in this way, it makes perfect sense that we would have all sorts of variation.
So, the real reason why we have dialects is actually because we arbitrarily choose one version of a language and deem that "the language", making every deviation from this official version a de facto dialect. In reality, we are a huge system of varying idiolects with varying levels of coherence.
Differences in language change today
There are certain things that drive a language towards greater and broader coherence nowadays. The biggest is education and a writing system. With everyone learning standard English in school, and a standard writing system, we maintain some connection to a certain version of a language that changes much more slowly and conservatively.
Another major factor that maintains widespread language coherence is media: books, radio, TV, Internet. On television, we hear a variety of different accents, and above all others, a "dialect-free" version of English. We can read books, webpages, and listen to the radio, and all of these things impact our own internal version of language.
For these reasons, language change in English might take a different form than it had for its entire existence until 100-200 years ago. It may be slower to change in certain ways, and faster in others, dialects may merge, or any number of other things.
Best Answer
There are two questions here, one about the phenomenon, is it actually the case that regional accents are disappearing, and the other, what is the cause of such disappearance.
It is incontrovertible that accents (and entire languages) are disappearing. The articles you give links to refer to scientific articles that show that fewer and fewer people are speaking like their grandparents and more likely to speak the standard accent. There are many ways to show that an accent is going away but the simplest is simply a single point of many possible, the loss of post-vocalic 'r' in England.
From 'Why r is not always pronounced in England'.
This picture shows the accents with 'r' in England, in the 1950's on the left and the 2000's on the right. There is a noticeable loss of people who don't drop the 'r'. A way to describe this is that the regional accents in England are becoming less distinct which is to say disappearing. Surely this is only one specific phenomenon, but it is one of many. There may still currently be a West Country pirate-like accent with its strong r's, but fewer and fewer people are speaking like that. Similarly, but in the other direction on the other side of the Atlantic, Boston or New York area or Southern accents which were traditionally r-less, are more likely to pronounce all their r's.
But this all shows that there is evidence that some features are being lost in a very general sense. There's also incontrovertible evidence that full languages, not just minor variants, are going extinct now around the world. So maybe you're asking if, specifically for English, whether of the the many labeled varieties out there in the US and Canada, UK, Australia, and other places, if any of those have just ... gone away. Surely, Geordie and Scouse and West Country and Estuary are all still around (and from movies and TV seem to all be going strong). And Saturday Night Live seems to be the place to do previously unnoteworthy accents of California and Philadelphia. On the other hand, I've noticed that people from the Southern US on TV interviews tend to surprisingly not 'have' an accent (regular people, not politicians). What I'm saying with all this is that it is unclear if the named varieties are being washed away, or if their distinctions are being encouraged, if non-standard varieties are losing speakers or gaining. That, as John Lawler hinted at in one of his comments, would take a lot more comprehensive research.
As to why any of this may (or may not) be happening though, that is a different matter. (note that the link I gave is titled 'Why' but there is only description in the text, little causal analysis).
One thing that is sure is that populations that are nearby and speak with each other tend to share language features, even if they are from entirely historically different speech populations (see Sprachbund). So it is almost boring to explain loss of distinctions, and eventually loss of accents (and even entire languages) by appealing to mass communication and globalization. The socially more prestige accents tend to hang around longer than the low prestige varieties.