I've always been able to 'see through' personality tests. But I didn't get that so much with MBTI. I think it depends how well the questions are framed.
Also if you really want a representative answer, you will actively be aware of what you want to be and what you think you really are and simply force yourself to be honest. So for that reason, I do find the result I get useful because I know I believed that the answer I chose was the best available.
In terms of how far looking into a mirror can help (taking your points that its just telling you what you think you are), I think that can be enormously useful. One rarely sits down and maps out a holistic framework of one's strengths and weaknesses. Seeing it there can bring a lot of things to light. Furthermore the tests often probe you on categories that you haven't necessarily considered beforehand, which can provide additional insight.
As others have mentioned, one might have a good understanding of one's own dispositions without necessarily having much awareness of how other people work and function. Such a test can make you aware that things you thought were normal or universal are specific to you, and it can teach you a lot about why other people are the way they are and how you might come across to them.
Finally, of course we might all alter and get different results over time. If you use such a test assuming that its about unearthing some intrinsic authentic 'self' buried deep in your psyche, then yeh obviously that is a bit silly and naive. But if you see it as just a tool for introspection it can do what you want it to. And I think its very interesting to use something like that periodically over the course of your life to work out how you've developed and changed. This can actually be quite motivating when you discover that stuff you thought was intrinsic is actually fairly malleable.