This ignores the fact that there exists multiple meanings of bits *within the same context*, and that beginners likely can't tell them apart.
Feel free to try it yourself - talk about Bitcoin "bits" of a particular value with somebody who doesn't understand Bitcoin. Then explain that the cryptography uses 256 bit keys. I would be surprised if you could find somebody who would not be confused by that.
Let's say a website says a song is 24 bits. Was that 24 bit audio resolution or 24 bit price? Somebody writes about 256 bit keys, are that their size or value?
You guys here can probably tell the difference. Can everybody...? Bits will cause confusion, because plenty of people will not be able to tell these apart. They will not know WHEN to apply one definition or the other.