The pithy answer is that historical perspective matters because without it, the tendency of your mind will be to draw conclusions based on an the limits of your own experience.
The dumbest example would be that if you’re only familiar with raspberries, there’s a good chance that you’ll infer that all red berries are delicious and healthy. The moment that you would encounter some poisonous red berries, you would eat them, and then you would die. With outside knowledge of different types of red berry, you’re less likely to make a false generalization.
This is what most thinking people do today: search for tiny pieces of context-free novel information which makes them feel good, draw inappropriate inferences from those tiny pieces, and then suffer when those conclusions turn out to be false.
It’s the same way with everything else, but attempts to turn all areas of human knowledge into a ‘science,’ regardless of the limitations and difficulties involved in science as it relates to human societies, has made it so that people, especially modern political leaders, tend to value the particularized, memorization-heavy, language-dependent, and innately subjective discipline of history. Instead, the hope has been to replace subjective history with objective social science. It’s not incidental that Marx and Engels considered history to be a science, and one that they had perfected.
Historical perspective matters in politics because many of the same issues come up many times through history, and the mistakes that leaders and the general population make tend to share similar characteristics.
Even for business people and technicians, knowledge of history helps in building a general understanding of how what you create and discover will land upon the public. It also helps in parsing out what is a social development and what is truly a scientific-technological development.
One of the reasons that Americans are the way that they are (and modern people in general), often bedazzled by what seem to be continually new developments, is because all developments are entirely new from their limited, childlike perspective. Certainly, this hasn’t always been the case — the founding generation and a couple of generations afterwards were deeply knowledgeable about both ancient and more recent history — but historical amnesia and a burning faith in the explanatory power of the social sciences are characteristic of westerners from the 20th century onward.
The top problem bedeviling most contemporary conservatives is that, not only do they conserve nothing, but they have no idea what it is that they are supposed to be conserving. It could at least be said that conservatives of the 1950s and 1960s knew the Bible, but it seems that today that it is mostly used as a prop for selfies and a source of cherry-picked and re-interpreted quotes rather than a cultural pillar.
People find themselves adrift in the present time, with few references about past events, and an extreme, obsessive focus on the lives of trivial people and unimportant events that just happen to be occurring now. Since there is no skeleton of historical context in the minds of the modern people, the only thing that they have is what draws their attention in the moment, which is usually some irrelevant plane crash, a pornographic video featuring a famous person, or the sad discovery of a slut’s corpse in a dumpster.
Just because something is happening now does not make it relevant, important, or even interesting. You study history because it gives you a chance to learn from the people who came before you, and to provide you with context that helps you to make more intelligent decisions. For some, the study is also inherently pleasurable, especially because the stories that have survived the indifference of the ages tend to be compelling ones.