I have always felt that the Supergirl stories before she was adopted by the Danvers are some of the lamest (and most juvenile) of all DC superhero comics of the late 1950s/early 1960s, although I must admit she has some pretty stiff competition from most of the contemporary Wonder Woman comics, and some of the more outlandish Batman stories.
Supervillains - or indeed any villains - are usually noticeable by their absence in this period, and stories revolving around Supergirl/Linda helping other orphans to get adopted, or solving their insignificant problems make for mind-numbing, boring reading - at least to this reader.
I prefer the Superman Family period of Supergirl most of all, when she left college and started working, particularly the Elliott S. Maggin and Jack C. Harris stories, even allowing for the fact that most featured the horrible inks of Vince Colletta.
I second and agree with everything you just said. Those SUPERMAN FAMILY backups were terrific. A special shout-out should be given also to Marty Pasko's Supergirl stories, like "The Girl with the See-Thru Mind."
I always found Supergirl an enormously appealing character, more so even than Superman at the gut-level: A teen-aged girl who could break open the head of the toughest DC bad guy, but also with a genuinely sweet personality who would burst into tears if a boy gave her flowers.
Supergirl is an emotional person, but I can't see her for a second crying because a boy gave her flowers. That girl is a very, very tough person.
It's only retroactively, by guys that don't understand the character like Alan Moore, did she become "Gidget."
Awkwardness with superpowers
Also another characteristic someone as competent as Supergirl does not have.
It would have been great to send her on a couple of dates with a Reggie type.... "If looks could kill...."
There are many characters I can see as dating jerks. Pre-Englehart Scarlet Witch, for instance, comes to mind, because she was impressionable and not a very assertive person (which changed when she got the courage to admit she loved an artificial man).
Supergirl is very, very low on that list as well. Like I said, she's tough.