This is accurate.
For public companies, the quant part has been calculated by the market. Everything that remains is, almost by definition, in the realm of the irrational, unknowable and/or political (usually at the Board level, though government factors could also be involved).
And then you go on to say "everything that remains is ... in the realm of the irrational", everything you have laid out is in the realm of the irrational. Including the market.
This discussion devolves into useless semantics if we rely on colloquial definitions. In case it wasn't clear, the predictable, explicable parts of a public company's value are generally priced in by the market. (If they're not, we're in a chaotic environment and nobody's doing classic M&A.) It's the other stuff, which we put in a bucket titled "irrational," M&A bankers address.
This is why the cash-flow models bankers prepare are largely performative. Every buyer builds their own models. And most of the time, the market does the modeling for them. The part the market can't model, the things one seeks to do with control, is the main attraction.
I caveated the comment because private company M&A is different. There, the negotiation does focus on valuation. Quality of assets. Current cash flows. Strength of contracts. Discount rates tied to the actual cost of financing versus an MBA model. While public company M&A dresses financial strengths and weaknesses in the language of partnerships, private company M&A seeks to address political issues (e.g. a senile founder with voting control) through talk of fundamentals.
The other side is also not necessarily irrational, but much less deterministic. For example, there is the question if the board even wants to sell, if they like the potential buyer, if they have a vision for the company that aligns with the buyer and some non-tangibles. Charisma projection and speech-craft definitely has an influence too, as has track record.
The more factors are in alignment with the board, the closer the price is to the stock value. The more hostile the negotiation, the more it moves away.
An econ 101 trope about the value of stock ties it to the value of future dividends. This is technically correct, but practically useless. You don't get those dividends unless the Board gives them to you, and investing on the hope that a Board throws you candy is just a hair short of stupid.
The real enforcer of value in the markets is M&A. In M&A, you become the board. If there are cash flows, you can take them. If there aren't, you can't. You're playing a game of looking for things the market and/or management missed or couldn't access. Furthermore, the moment that process starts, the moment negotiations become public, smart people focus on the stock to anticipate those terms. If they think another buyer could see cash flows you don't, they'll bid it up and the Board will take the signal (as will those other buyers and their bankers); if they don't, if post announcement the stock keeps trading below the bid, the Board will take the hint.
It's Musk, so you can throw out the book. He just takes the stock value and then tweaks it so that the offer contains 420 because obviously that's his shtick since some time.
Wonder if the SEC will ever live that one down.
Musk's Twitter takeover is a textbook LBO transaction. The negotiations were unorthodox. But that's been true of LBOs since the 80s. Usually the bankers were the ones up to the antics; this time it's the principal.