Superman #149: The Death of Superman! is proof that Superman had a good reason to keep the existence of Supergirl secret until she was ready. Lex Luthor manages to murder Superman, but he doesn't get away with it because Kara captures him. And she was able to capture him because he didn't know of her existence.
Supergirl grew up during this period (she was 15 when she first appeared and became a young woman in her early twenties before being quietly deaged to 19 in The '80s) whereas Superman remained fairly static. Later storylines have established that Kryptonians age more slowly under a yellow sun after reaching adulthood, so it makes sense she got older although her cousin did not.
Post-Crisis
The Pocket Universe "Matrix" Supergirl's being a protoplasmic artificial life-form created by Lex Luthor makes a lot more sense considering how Lex's Silver Age origin involved him creating a protoplasmic artificial life form that was accidentally destroyed by Superboy in the accident that cost Lex his hair.
While not so much subtext as text, Matrix Supergirl's relationship with Lex Luthor is easy to understand with the fact he looks identical to her creator as well as being a Villain with Good Publicity. Its easy to understand a Naïve Newcomer like Matrix being susceptible to the wiles of someone like Lex.
Some people balked at Many Happy Returns having the Pre-Crisis Superman choose Linda over Lois Lane. Then you have to remember the Lois Lane of the Silver Age was not the intelligent hard-bitten reporter of both before and after but a silly Stalker with a Crush always trying to figure out Superman's secret identity. Linda, by contrast, was a sane and sensible young woman with a strong heroic streak after years of character development in her books.
Speaking of which, it's easy to understand why Linda's plan to replace Kara Zor-El in the Crisis On Infinite Earth's failed. Linda isn't nearly as powerful as the Pre-Crisis Supergirl, possessing only a fraction of her powers.
New 52
It becomes a lot more understandable Supergirl wouldn't trust Clark initially given the Rip Van Winkle effect she's undergoing, the craziness of his claims, and the fact he actually talks in very bad Kryptonian. Also, the fact he could be a clone or genetically engineered figure. Indeed, this is exactly what H'El turns out to be.
