No, the test itself is definitely the problem. Regardless of whether you believe a personality type test can be effective, the MBTI is particularly and provably ineffective in just about every measurable way:

It's not reliable. It has terrible test-retest reliability. If I'm X personality type, I shouldn't test as X type one time, and Y type the next, and Z 6 months laters.

It's not predictive. If a personality test accurately judges someone, it should mean you now know something about someone's behaviours, and can extrapolate that forwards and predict behavioural trends. MBTI does not.

It fundamentally doesn't match the data. MBTI relies upon the idea that people fall neatly into binary buckets (introverted vs extroverted, thinking vs feeling, etc). But the majority of people don't, and test with MBTI scores close to the line the test draws, following a normal distribution. So the line separating two sides of a bell curve ends up being arbitrary.

And finally, it's pushed very hard by the Myers-Briggs foundation, and not at all by independent scientific bodies. copying straight from wikipedia:

Most of the research supporting the MBTI's validity has been produced by the Center for Applications of Psychological Type, an organization run by the Myers–Briggs Foundation, and published in the center's own journal, the Journal of Psychological Type (JPT),