Its not about cold/hot, its about the method of generating.. I should have been clearer.

Your private key has 128bits of security even though it is 256bits long. That's the bar. Go any higher and it is just easier to guess your private keys than it is to guess your mnemonic.

Great.

If you used bias dice or coins, and create 12 words, you will be under 128bits, but mathematicians have already discovered that the effect of the bias is greatly reduced over many rolls/flips.

Same would apply to a computer, but even if you had vetted, open source software, there are so many layers that could be inserting bias, including hardware, and yes they often use many sources to offset the risk, but you don't know what you don't know. So I make no assumption other than that a computer generated set of words is always biased but _probably_ not enough to score lower than 128bits of entropy with 24 words.

I suggested 15 because if we assume SOME bias but just nothing malicious, then we get over 128bits of security.

But I'm a stickler for the details... in reality, 12 words is probably always good enough... that and DON'T MAKE YOURSELF A TARGET.