The Wars of the Roses were not devastating.
The Wars of the Roses were not a particularly bloody affair; Edward IV reportedly told a Burgundian writer, Phillip de Commynes, that as soon has he felt victory at hand he would order his troops to spare the common soldiers on the other side in order to preserve his popularity. This of course, doesn't really gel with one of the popular factoids about the period, that Towton was the bloodiest battle on English soil. But this misses the point - the brutality of Towton is shocking because it was the exception, not the rule (compare Barnet and Tewkesbury). This also extended to the aristocracy - whilst many individual elites certainly lost their lives in reality most noble families survived the period; the despondent claims of the likes of Thomas More that half the nobility of England had been wiped out were simply not true. The rate of extinction for noble families did not change at all during the Wars of the Roses. In all the period of actual campaigning was probably only about a year.
Throughout the later middle ages castles in England became increasingly residential, undefended and geared towards comfort (contrast France during the Hundred Years War); they were no longer the great fortresses that characterised the reign of Edward I. Now, there are obviously caveats to this - castles of an earlier period were by no means uncomfortable and historians now recognise they served more than just a purely military purpose. Furthermore, many of the aristocratic residences of the 15th century were still in many ways, recognisable as castles. These are important points, but, nevertheless the point stands that the aristocracy appear to have been no more nervous, overall, about warfare during the Wars of the Roses than they had been previously. This is also true of the towns, who spent very little money on their defences during this period; indeed there were actually less grants to build defences during the 15th century than the 14th.
The popular myth of the Wars of the Roses is derived, of course, from Shakespeare. It's from Shakespeare that we get our view of the wars as a period of terrible violence and bloodshed. Obviously Shakespeare had his sources who worked to build up the bloody legend of the wars before he ever put pen to paper - Thomas More, for example. However it is at Shakespeare's feet that we can squarely lay the blame for the popular conception of the period as resembling the average death metal album cover.
The Wars of the Roses were more like a series of battles fought sporadically than a true war. These battles could be bloody and led to political instability. But there were also long stretches of stability and prosperity under, for example, Edward IV and some continental observers looked at England approvingly. The wars proceeded in a very circumscribed manner and the violence did not meaningfully impact the overwhelming majority of the population. The Wars of the Roses were indeed, as you said, simply a war between two branches of the Plantagenet dynasty over the throne. Medieval England had civil wars prior to this, it had dynastic civil wars prior to this. The Wars of the Roses only begin to loom larger than life due to the Tudor-centric worldview of 16th century writers and the tendency of modern historians to associate the rise of the Tudors with the end of the English middle ages.
As for the notion that they don't see much light, this simply isn't true. The BBC have produced two major historical dramas set during the period recently. The discovery of Richard III's body and his subsequent re-internment were major news items. There are enough popular histories of the period to give Caxton nightmares. There is an extremely ugly memorial that was recently put up at Bosworth field. The battle of Bosworth re-enactment is well attended. The period is taught in schools. I could go on, but it is, arguably, the most well known aspect of the English middle ages in the UK.
If nominations are open for "most devastating civil war in England's history", I think the gold medal (immediately melted down to pay mercenaries) should go to the Unlaw, the civil war in England and Normandy off and on between 1135 - 1153, between Matilda the Empress and Stephen of Blois. Barons seizing power, private wars, breakdown of royal authority ... If England hadn't then gotten our Henry II, I don't know what would have become of England.
Yet the Wars of the Roses has this reputation. Lloyd George in 1917 thought that Britain's losses so far in the First World War were "greater than those she had sustained in the aggregate in all her wars put together since the Wars of the Roses".
A notable book was John Gillingham, The Wars of the Roses, 1981, addressed this, especially in the first three chapters: "Introduction: The Making of the Myth", "This Seat of Peace", and "The Disciplines of War". (Some lay readers complain that the later and larger parts, a narrative history of the war, was confusing. I find it highly readable.) He felt that a lot of the traditional opinion was because of Tudor-era propaganda, like Shakespeare, Thomas More, Edward Hall, and such.
(Source for this part: "Historiography" in Keith Dockray, Henry VI, Margaret of Anjou and the Wars of the Roses.) Gillingham followed the earlier lead of C. L. Kingsford and K. B. MacFarlane. Kingsford and Gillingham felt that the impact was far smaller than previously thought. McFarlane, in his final lecture, said that he didn't even think it was a dynastic war at heart, or over-mighty subjects, or the loss of the Hundred Years War, et cetera, just that "Henry VI's head was too small for his father's crown ... the nobility was unable to rescue the kingdom from the consequences of Henry VI's inanity by any other means".
They may be going too far in implying "tain't no big thang", but they do muster a lot of evidence suggesting that, while there was disorder and breakdown of government, it wasn't devastating. Maybe the total amount of warfare didn't amount to just 12 weeks over 1450-1485 (W. H. Dunham), but it was more like a year in aggregate. Noble lines didn't die off at a noticeably larger rate than before or after, though individual lords might be killed. (Yet William Tyndale wrote in the 16th C, "Of their noble blood remaineth not the third, nor I believe the sixth, yea - and if I durst be so bold - I wene I might safely swear that there remaineth not the sixteenth part.") English towns had been dropping their defence expenditures for decades, and they continued to drop. Philip de Commynes from Burgundy, who had seen plenty of war, at the time commented that the English were "of all the people in the world most inclined to give battle ... If any conflict breaks out in England one or other of the rivals is master within ten days or less. Our affairs, however, are not conducted in this fashion." The decisive battle, Bosworth Field: most of the English nobility preferred to stay home, and it was decided by one man.
But that's just addressing the premise. The basic question was: Why doesn't it get much attention today, other than inspiring some aspects of the start of Game of Thrones?
For my second non-answer of the day so far: uh, I dunno? Maybe people buy into the Tudor-era myth and think, like Bishop Stubbs, the entire era is all too depressing? For example, Dunkirk and the Battle of Britain get attention and were bad for the UK, but at least a few years later there was a semblance of a happy ending for them.
Great question!