I know that according to traditional finance, firm-specific risk plays no role in the pricing of an asset but only systematic risk. On the other hand, the stock price should reflect all discounted future cash flows of a firm. If a firm screws up now through spilling oil in the water for example, then, in reality, the stock price will most likely decrease but according to traditional finance, it wouldn't. Where is the sense in that, I wonder? Such as theory, that firm-specific risk doesn't influence price is against all intuition, isn't it? I mean even if all investors hold perfectly diversified portfolios, spilling oil in drinking water should still reduce your market valuation, shouldn't it?
...but according to traditional finance it wouldn't.
If valuation is about discounting expected future cash flows, then after an oil spill, investors expect hefty fines, i.e. cash outflow, hence the PV is lower.
I think the important is the word expected - you don't know what the actual cash flows going to be (at least not with 100% accuracy), you are only expecting (i.e. it's a probability distribution with perhaps some fat tails).
I think that there are two points to be made here. First, the distinction between returns and price. Secondly, the agnosticism of quantitative finance to upside versus downside risks.
"Idiosyncratic" firm risks should be reflected in the price such that its returns are capital are independent of idiosyncratic risk. Therefore, returns are only a function of "systemic" market risks. For example, the risks of your oil spilling firm would be discounted in the market value of its assets. The expected returns of a long position in such a firm should be commensurate only with market risk.
Furthermore, most of quantitative finance is built on the no arbitrage principle; it is assumed that an efficient market already factors idiosyncratic risks into price. This lead to the concept of risk neutral pricing, meaning that normative economic models of a firm typically do not differentiate between the types of risk; i.e., risk is symmetrical. In your example, the risk of a company which is exposed to oil spills would be reflected in the volatility of its assets and/or cash flows wherein notions of volatility are symmetrical.
I think your aversion to defining risk this is natural because, in colloquial language, the use of the word "risk" is usually meant to mean exposure to downside events and probabilities, whereas "opportunity" usually mean exposure to upside risks. Again, the word risk is usually not used this way in quantitative finance.