Studies like this are done all the time.
Not in psychology they aren't.
Studying human behavior is considerably different than testing the effectiveness of a drug vs a placebo (something a double-blind study might be appropriate for). That's one reason it is difficult to construct valid and reliable tests of personality.
Just the basic idea of taking 3000 people (a sample you just can't get) and giving 1000 of them accurate test results, 1000 of them inaccurate results, and 1000 of them no test results, and then looking at them 5 years later to see if they are "happy" or "successful" in their careers, and then attributing any differences between these groups solely to the test results they were or weren't given, is downright absurd. How happy or successful those people reported they were 5 years later would likely have been determined by a multitude of factors, none of which would likely be related to those test results. How would you eliminate, or control for, all those other factors, besides those test scores, that would have affected happiness or success?
You really don't understand scientific methodology as it used in psychology. When you study the influence of one variable (i.e. test results) on behavior (i.e. career choice), you must control for the influence of all other variables on that same behavior, and you cannot magically do that with "statistics"--you must control those other variables by eliminating them in some way, or by holding them constant for all subjects. Reality dictates that all those other variables cannot be controlled in the sort of study you propose. You are dealing in fantasy, not reality, and you are not fully acquainted with scientific methodology in this area of study.
Do you realize it would be unethical to give subjects inaccurate test scores, about their own personality traits, and then further compound that unethical practice by giving them fraudulent career counseling?
And then you want to measure whether these subjects are happy or successful, years later, based on the false information you have given them?
You cannot deliberately mislead research subjects, in psychology, in any way which can potentially harm them--that is unethical. Giving someone false information about their own personality traits, based on false test scores, would definitely be construed as harmful.
At some point, probably before that person even left the room after being given those false test results, the person conducting this "experiment" would have to tell the subject the truth--that the results were not accurate. You would need to de-brief the subject and make sure that they were not unduly distressed by the false information they were given.
Test construction is a challenging enterprise in psychology. Test validity and reliability are accomplished in various ways, but the use of the "experimental method" really would not be among them.
What is the big deal if people want to take or use the Myers-Briggs test? No one claims the test is 100% accurate, or even 60% accurate. It is not intended to predict anything. The test can yield some information about an individual's personality traits. People might find such information useful. If some people didn't find this test useful, in some way, why is there even a market for it?
I honestly don't understand why you are so concerned about this particular test. No one is forcing you to either buy it or take it.