Why Hilda x David works and David x Frida doesn't.
It's simple really.
Frida is uptight, bossy, and treats David like a little brother.
Hilda is kind, encouraging, and treats David like an equal.
Frida's friendship with David has been completely stagnant since they met. Frida may have protected David when he was scared, but never did anything to help him overcome his fears.
Hilda has helped David to grow as a person and overcome most of his fears, to the point where he is a completely different character by the start of Season 3.
In short, David has much better chemistry with Hilda than he ever did with Frida. Hilda is the driving force behind David's entire character arc. She has always inspired David to step up and take initiative through her actions alone.
A prime example of this is in the series finale. When David expresses reservations about approaching the fairy mound, Frida just waves his concerns aside with a condescending line: "You're not the one going into it, David. Hilda is." This just makes David feel worse. Hilda, on the other hand, places a reassuring hand on his shoulder, and simply tells him: "David, I need you."
A smile and a few simple words of encouragement from Hilda are all it takes to strengthen David's resolve, and later pays off when David risks his life to rescue Hilda from the fairy mound.
Frida puts him down. Hilda lifts him up.
