Not dissimilar with the way a "psychic" will use Cold Reading to construct a profile of a client - though their preferred method is to produce statements that will apply to 90% of the population through saying both one thing AND the opposite. Like "you are a thrifty person, but sometimes you tend to splurge". Bet pretty much everyone will agree with that!
I think to an extent there's a reason for that. People who seek cold readings tend to seek direction, perhaps help make decisions or even to better understand themselves and their lives and of course the cold reader themselves is being deceptive. But I'd argue people seek something similar through psychology, but rather than attempt to make fairly universal statements where people add their own meaning, psychology in some ways attempts to categorise people's way of thinking and also offer explanations behind our mind and behaviour. Not to mention, cold reading is basic use of psychology, though deceptive. But the study of psychology often suffers difficulty when it comes to individual differences, meaning in psychology universalization is very difficult.
I would say Jung's personality profiling is still generalised, but it is an attempt to categorise how people think and behave. Of course, since Jung was around there have been larger developments in psychology and a lot more complexities, with his works partially as an inspiration (he was highly significant, though not as well remembered as Freud). I think these profiles should work as a nice starting point and can be used to help a person assess their own personality and identify strengths and weaknesses. The tests are based on the data you give rather than on randomisation and universal statements, even if they are still generalised.
The profiling it gives me, INTP, is actually surprisingly accurate. Of course, it's not highly specific, but enough to be able to categorise my characteristics and make factual statements about my personality and statements that not everybody can put their hand up and say, "that's me". In reality, what they're doing is taking 4 key categories that best apply to you and merging them together to form a type.
Basically I am curious, imaginative, analytical, critical, tolerant, precise, hesitant, I like to make sure I have properly looked at something before making a judgment, look at things in depth, striving for precise and efficient communication. This is a pretty accurate summation, because these are all things I already knew about myself, but then I am highly critical of myself and tend to overanalyse, so I have thought about it myself.
Of course, as a cold reader, you could probably sell some of those traits if you're good at what you do, all a cold reader needs to do is put these things into context and bring you to focus on a moment, even if that trait doesn't necessarily apply to you as a person. Let's take 'tolerant' for example, now, I am a highly tolerant person, despite how critical I am of them, I am tolerant of religious folks (who are probably the people I'm most critical of). But if I were an intolerant person, all a cold reader would need to do is work as a spin doctor to make their inaccurate statement, accurate. They might say something like, "you've been in situations where you've been uncomfortable and something hasn't set right with your core beliefs, but you've kept your mouth shut to tolerate the situation", the person will probably nod because there's a high chance they've been tolerant of something in their lives, then when the person nods, then they will pursue it further in order to put a spin on the situation to make a judgment of character, if this person is gullible or egotistical enough, they may think they're a tolerant person, despite their dislike for Canadians. It's about influencing how you look at yourself and influencing how you think about any situations. It's kind of similar to what Elizabeth Loftus found in her Eye Witness Testimony experiments, where the wording of a question affects how a person recalls an event. Similarly with studies into reconstructive memory.
So, how is this any different? It's an attempt to categorise human personalities, just as some writers have attempting to categorise stories into 7 basic plots. It's picking common traits among personality types. The answer rely on the information you personally give. The point of the tests (and there's different versions) is just to determine which category you best fit into. Why do it? It's a starting point and there's certain things that help people in your category that may be relevant or help you. Typically with these profiles people tend to think more about the kind of jobs that suit them. In that regard, the tests have also been pretty accurate too. The main things I've thought about going into: teaching in higher education, Chemistry, Psychology, Programming/Software development, writing/journalism/editing, 3D artist, Historian/Archaeologist, which tick the right INTP boxes. Sadly, I work in customer service.
The career I am pursuing is the writing/journalism/editing one.