No, not really. A lot of people died in the First World War, cutting across class lines. The guests of honor at the ceremony dedicating the Tomb of the Unknown Warrior were 100 women who had all lost their husbands and all their sons in the war. JRR Tolkein later wrote one of his sons "By 1918 all but one of my closest friends were dead."

So, yes, some people did lose their eldest sons. But inheritance laws rarely allow anything to go uninherited, especially if the person who would have been doing the bequeathing was still alive and able to make out a new will. Even if someone dies intestate there are rules on how an estate will be divided.

For instance, Raymond Asquith, son of Prime Minister HH Asquith, was killed in the war -- but he already had two daughters and a son. His brother in law, Edward Horner, was also killed in the war. But when Horner's father died, Asquith's wife inherited the family seat of Mells Manor.

What really happened to the great houses of Europe, especially Britain, was more complex than simply a lot of heirs dying.

The power and wealth of the British elite was based in their ownership of land. For most of them that meant they had an income based on renting their land out to tenants to farm cash and staple crops (a few, like the Grosvenor family -- now the Dukes of Westminster -- owned land in more urban areas and developed it accordingly). Some invested their income in stocks and bonds, but for the most part it was spent on maintaining one or more country houses, a townhouse in London, entertaining their fellows and travel to the Continent and even America. All this was done for politics, for social climbing and making sure your children associated with people of their own class.

However, beginning with the repeal of the Corn Laws in 1846, things began to slowly change. By the 1870s, advances in transportation resulted in a steep fall in agricultural profits for the tenant farmers and a reduction in agricultural employment. In the late 19th century the British government introduced death duties on inheritance, partially as a way of breaking up the large estates, and it was increased during World War One and especially after Labour came to power after World War Two.

Both wars also caused manpower shortages in the big houses, all of which needed a decent staff to maintain them.

Incomes fell, capital was reduced by taxation and last of all, Britain went off the gold standard during the War for the first time since the Napoleonic Wars and has never looked back (except briefly under Winston Churchill in the 1920s, which was disastrous), which resulted in inflation and free exchange rates changing the value of the pound sterling.

Certainly by the 20s, if not before, economic power had passed to banking and industry. Publically traded limited liability corporations were the future.

TLDR, the old upper classes were undone not because of failure-of-issue but because of social, legal and economic change that began in the 1840s.