They don’t quite say that Lamborghini was the only one producing supercars; they say that other makers conceded the market in terms of sheer extremism, especially when it came to appearance.
In head-to-head comparisons of actual performance, there wasn’t really much difference between the Countach and other high-end sports cars like the Ferrari Berlinetta Boxer and its successor, the Testarossa. The Porsche 911 Turbo had a reputation for being incredibly frightening to drive, especially for the inexperienced, and it was at least as fast as the Lamborghini through most of the key acceleration points (0-60, quarter mile, etc.). Even the Aston Martin Vantage of the early 1980s kept pace with the Countach in a straight line in this 1984 comparison.
I worshipped the Countach when i was a kid, but it was really the looks that set it apart. Most reviews, especially modern reviews that evaluate the Countach in light of recent developments, are critical of its crappy driving position, terrible visibility anywhere except straight ahead, and sheer annoyances when driven anywhere except a deserted open road. Many similar criticisms were leveled at V12 Ferraris in the 1970s and 1980s.
As for the OP’s question, others are right that exotic cars tend to be better put together and more mechanically reliable these days, partly as a result of corporate ownership and the quality control that has come with it. Also, the expansion of the market, with so many wealthy people (especially younger ones) able to afford these cars, has made quality control more important.
Most people who buy cars like this put a couple of thousand miles a year on them, at most, and generally put those miles on while cruising city streets, heading to or from a Cars and Coffee meeting, or making a Sunday afternoon drive to the beach. Very few owners track their cars, or even come close to testing their performance limits. They buy them for their looks and their cachet, and when they spend a quarter-mil on a two-seater embodiment of their net worth, they don’t want it breaking down in traffic or otherwise embarrassing them with shitty panel fit or oil leaks.
This is something of an exaggeration. It applies to the limited-run hypercars like the LaFerrari or the 599XX, where you need a prior relationship with the maker to be considered, but not to the more common models like the F430/458/488 model progression. Porsche does something similar for its limited-run cars like the 918, the 911GT3RS, the 911R, etc.
That’s not to say that it’s always easy to buy a new Ferrari, even of the base models. But this is simply a matter of supply and demand. As more people, especially more young people, have lots of money, demand for Ferraris has risen faster than production, and it’s Ferrari dealers (not the factory) that tend to give priority to long-standing customers. But anyone can put their name on the waiting list, and when the established customers have their cars, if there are still new Ferraris available, you will be able to buy one even if you’ve never owned one before. A few years ago, there were dealers having trouble moving some of their Ferrari Californias, because it wasn’t really a popular car by Ferrari standards.