Honestly, Frozen Heart is probably a bad example for this, as it is cost efficient even without mana.
Sometimes, you can justify buying items with useless stats because they still synergize with you very well or suit the situation. As examples, Liandry's Torment on Mundo (who was one tiny AP ration), Nashor's Tooth on Azir (when his solders don't apply the on-hit effect), and Wit's End on Irelia (when the magic resistance reduction only affects her E).
You should always ask yourself WHY you are building an item. The answer should never be "well because it's good" or "because i need that one stat." You need to maximize your potential in the game to be the biggest threat possible.
I would NEVER buy liandry's on mundo. There is pretty much no reason to ever do that. You are a bigger threat by having HP/MR/Armor from an item rather than the slim dps buff.
Nashor's on Azir is viable imo and infact i do build it on him, but the damage on hit is not completely useless. It's just not used as much.
As for the irelia Wit's end thing, i don't understand your point. You can use it on her, but no way in hell should you build it against her. Unless you are magic damage auto attack dependant (like warwick?) BOTRK would be a million times better than the minor MR debuff you'd bring to the fight.