I disagree. For the largest derivatives markets -- a: interest rate swaps, b: FX swaps, and c: credit default swaps, they formed (and grew) because market participants wanted to express a particular view, but could not easily find enough of the required "cash product" -- a:gov't bonds, b:spot FX (or simultaneous, dual currency, short-term LIBOR lending), c:corporate bonds. For (a) and more so (c), it is difficult to short, even for large/institutional clients. Synthetic equivalents (interest rate swaps are _effectively_ synthetic gov't bonds) 1:can be created upon demand, specific to a client's needs, and 2:can be trivially shorted.
When a client is buying or selling a derivative, they don't care about the notional -- they care about the delta (or gamma/other greek). You just turn the dial for notional to achieve the target delta/gamma.
Your second sentence does not make sense with respect to single name equity options. (I pick a simple product as a counterpoint.) I doubt anyone is losing sleep in 2021 over 'rho' (interest rate sensitivity) in their options trading book for any floating currency with short term rates below 1%. Thus, everything about the underlying price (including expected future divs and its historical volatility) drives the prices of single name equity options. (If you are referring to delta one derivatives, that is a whole different discussion. And yes, they trade -- equity swaps, because you can get implied leverage through financing.)