Baird,
There's a difference between instruments that are meant to reveal truth and instruments that are meant to be used as a personal tool. Based on your comment here I did a quick Google Scholar search and realized that you and I are in the same field -- my apologies for not realizing it sooner.
I'd love to hear more about the scale you developed (one of my respected teachers had a great deal to say about the necessity of convergence between self and other-report measures).
As a note, however; in research and clinical practice we put a premium on the ability of our scales to reveal a highly accurate (and reliable) picture of someone's personality to guide our behavior as scientists and therapists.
I'm not sure that people in the real world use personality quizzes in the same way. I do think it's problematic that people can control the results, but note that for the vast majority of people--who must have intuitions about the controllability of such quizzes--the ability to pick the result they want doesn't deter them much from using the quiz.
I've been thinking about that as I wrote this article. I think there is a degree to which inaccurate self-quizzes are still useful to people precisely because they are tentative and not to be trusted. I think they may serve a facilitative role in helping people learn about themselves by being deniable. A person can use them to test themselves, in essence, to see what they like and what they do not. Sort of like trying on clothes to see what fits best. If they like what they see, they own it. If they don't, the quiz was "just one of those stupid internet quizzes."
So maybe the inaccuracy itself helps people construct their identities, by forming the raw basis of the stories they tell about themselves (i.e. "that time I took a test and found out I'm an ambivert") and also that they hash out with others over conversation.
There's a reason the Cosmo quizzes were so insanely popular right from the start, after all.
It's a worthwhile check on the intuitions of scientists who assume their own approach to understanding such things is the default, or correct, approach. I suppose in this case that might be literally true, since the first personality quizzes were developed by resesarch psychologists, and the first Cosmo personality quiz was also developed by a psychologist. But I think there's a lot of wisdom in how people co-opted the quizzes and rapidly proliferated and started to use non-scientific versions for their own ends.
I've found that holds true as a rule of thumb, actually. There is great wisdom hidden in the way that most people do things. It keeps me humble to realize that scientists are the ones who made a self-conscious tradeoff, adopting a divergent set of principles because they are useful--though the tradeoff is that in some instances they are more brittle.