The cost of a card isn’t something that can be calculated, quite frankly. If I apply your logic to other cards, Dawn’s Eye should cost 13 mana or more because it’s several Imperial Mechanysts and two Staffs of Y’kir on one card. Radiant Standard doesn’t cost 12 mana either, even when it summons three 3 mana minions on top of a Snowpiercer-level Attack buff.
When a card costs so high, the value of each mana it costs also rises. I wouldn’t say the scaling is exponential, but it should be quite dramatic, or else there isn’t much incentive to use so much mana in a single card instead of separated assets. Caladbolg is an example of such a card when its effect should be powerful enough to compensate for the disadvantage a player needs to put him/herself in for playing an artifact that costs 8 mana. I obviously cannot determine how powerful the card will actually be, but I at least can judge it won’t be as overpowered as you make it out to be.