Perhaps her not being a love interest is exactly why she is the coolest.
I think it's more that Zelda's characterization has been getting better as time goes on, with the exception of Twilight Princess.
First Gen, (not counting the cartoon), she had no personality at all.
LttP (and I'd put Link's Awakening here, although "Zelda" in this one is actually the first appearance of Malon as a direct dream substitute of Zelda... and she still had more lines and plot relevance as anything but a McGuffin than real Zelda had up to then), has maybe a couple lines that just involve her expositing what Link needs to do next.
Ocarina Zelda had her as a somewhat mischievous child for a short run. Sheik hardly counts, since Sheik never really did anything but grunt stoically, so you can't really infer much about the character from that.
Windwaker Zelda was the first one to really get a serious time to shine as a character, being a pushy, aggressive pirate, although she notably becomes much less of a character when she's actually being Princess Zelda.
Twilight Princess Zelda was notably hated for being just some pretty girl who sits in a tower the whole game bored and waiting for Link to save her the game to be over so she can go back to ruling with wisdom being bored while sitting on the throne "acting wise" when Midna actually had personality and was the fan favorite.
Skyward Sword Zelda, they finally learned this lesson and decided to give Zelda real characterization and give her an actual relationship with Link so that players actually have some investment in seeing Link get together with her in the end... and go with default "this is the girl you're supposed to want" relationship #2, the most popular from 10-15 years ago, the overly-cheerful osananajimi. (If she wasn't typecast as blonde or a light brunette with hair tubes by that point, I get the sense they would have made Zelda a pink-haired two-side-up ditzy type.)
Breath of the Wild's "class rep" personality type seems an odd one, since it's not the most popular, but then, the most popular at the time, thanks to OreImo, was just dating a little sister, which was obviously a bit much for Nintendo, so management probably gave them a little more leeway to use a less popular stereotype.
OcaTime
Ocarina of TimeDrawing each generation of ZeldaFirst gen
Legend of Zelda; Adventures of LinkMusou
Hyrule WarriorsToon
Wind WakerBre Wi
Breath of the WildSkywa
Skyward SwordTwiPrin
Twilight PrincessArtist*** Tri
Link to the Past
(this title has a typo and an invalid kanji - it should be "神".)