I think there's something to be said for strategic niches here. The coin has a bit less combat stats, but it fits a passive play style a lot better.
Frost queen requires you to get in an enemies face in order to generate gold. If you're losing the lane this could be very dangerous, meaning you might not be able to do that. Then you're not generating gold which makes things worse. It also does nothing for health sustain. The active is great, but more focused around creating picks than the coins general purpose active.
Face of the mountain similarly puts you in danger every time you want to use it. In order to get the gold, you have to get close enough to execute a minion, giving the enemy a chance to poke you. It comes with some healing, but only enough to offset some of the potential poke that comes from getting close to enemies. It also does nothing for mana regen, so depending on who you play you have a decent chance of running out of mana fast. The active fills such a different strategic role it's like comparing apples to oranges.
The coin fills the 3rd niche which involves sitting back, and helping your adc if they get into trouble. You don't need to do anything dangerous to generate gold, gold just happens to you. At the same time, if you do get into a fight it sustains both your health and mana, allowing you to stay in the lane a lot longer/indefinitely. In addition the active is great for team fights giving an instant speed boost to everyone nearby. Since the kind of champs that take coin are focused on engage/disengage, this active is heavily beneficial to those champs.
Tbh I've always found gold efficiency to be a bad metric because you don't just need raw stats. You need the stats/effects that benefit the champ you play, and the things you want to do with them.