Shouldn't "glissando" be between notes, rather than starting at the start of the first note?

When you put a glissando line connecting two notes, playback makes it start as soon as the first note starts. My intuition of a glissando is that it should be a way to transition between notes. Is the current playback a reflection of how it is typically read in classical music? If not, wouldn't it make sense for the glissando's playback effect to start, I don't know, two thirds into the duration of the first note? And if yes, wouldn't it make sense to have access to a switch between the two different ways to read it?
Additionally, if I try to force it to be right, by writing the starting note as two duration-tied notes with the glissando being attached to the second one, then it simply doesn't play. I guess I'd have to use a slur to mimic the tie... and I'd get that ugly repeated note. Then to fix that I guess I'd have to actually write the note as the next one that would be de facto performed in the glissando, and then edit its vertcal position so that it looks like the original note, and make any potential resulting accidentals invisible / missing accidentals cosmetic-only.