[2021] crucible cost?

I suppose you think you're just reaching your hand into the flames and picking up a searing hot 3500+F steel crucible? No, You created a mechanism to input and withdraw the crucible without getting your tender fleshy bits anywhere near that thing, and also to pour it into ingot casts/molds.

Moving parts = mechanical parts. Smooth movement that doesnt lead to sloshing molten steel = oil.

Depends entirely on the oil used, and the location of that oil in the aparatus being used.A swinging arm that you hang the crucible in for example has the crucible on the end of the arm, but the moving parts containing oil far away from the heat.

https://i.pinimg.com/originals/14/f0/49/14f0492e723d8d3078ab63be04e2f42b.jpg Take this as an example. The crucible is seated a a considerable distance from the moving parts; the radiant heat of the crucible isn't enough to burn the oil, though; only direct contact would.
https://i.pinimg.com/originals/b9/91/c0/b991c0a554de628cc4b3d610e3bc50e7.jpg this one is similar.

Kindof as Seftak said. When you're just casting tiny ingots in your backyard for shiggles, then sure, a pair of tongs you picked up somewhere or made yourself'll be just fine for picking up your 5lb crucible and it's 1lb of molten metal.. But when it comes to long term survival, minimizing injury and streamlining the process are big pluses when moving around 200+ lbs of superheated molten metal.

And at the end of the day, whether you view it as doing it with tongs or not, it's an end game recipe that unlocks a huge amount of end game top tier items for use- It's recipe using rarer materials like oil and mechanical parts is, if nothing else, normal gamification.