It's not supposed to teach you either of those things, nor does it claim to. It allows you to remember,
from memory, how to write a character just by thinking of a word, and likewise, remember the meaning of a character by looking at it. If you consider that it covers 2042 characters with up to 23 strokes, it's quite some accomplishment just to be able to do that in the relatively short timeframe it takes to complete the book.
Attempting to simultaneously learn multiple meanings and readings along with the writing of a character is unrealistic for anybody without a photographic memory. Mastering kanji is an organic process, and shouldn't even be attempted all at once. After completing Heisig, you have a complete index of characters in your mind that you can start to add other meanings and readings to far more easily than trying to cram the information into nothingness.
Through learning new words, reading, and continuing to study the characters, you will soon start to associate them with Japanese words with a range of different meanings and readings. Naturally, it takes some time, but what's important is that it sticks, something that scribbling out one character a million times, with absolutely no connection in your mind to lead you back to it, definitely doesn't.
I seem to make this argument all the time (hopefully a bit more articulately each time
), because I almost feel sorry for the people who don't use Heisig, but if people would rather scribble and forget, I can't really do anything about it. I'm just glad I found the book when I did.