every time a purchase is made on a product- a vote is cast, in essence. while its true that S + D is more complex than it is presented in some ways, you need to note that suppliers want to charge as much as they can without disrupting too many purchases. In a modern setting, a lot goes into finding out what that price is- take apple for example. They started the iphone (originally) @ 400 bucks later for iphone 2 they charged 200 bucks per phone. why is that? the simplest answer (or the supply side answer) is that they quantified their prices against competition, found their target market more clearly defined or maybe they
simply didn't sell as many units as predicted etc, etc. this or all these could explain the shift in price. on the other end of the spectrum.
if consumers are not purchasing a good or service, the simplest explanation is that it is over-priced and in order to get rid of units they need to drop those prices.
this is true for even, say, a black-and-white tv, is there a market for this? i'm not sure, but even below marginal cost is there a price that is both profitable and appealing to consumers? probably not.
again, every purchase made, and even non-purchases when the possibility is present are fairly tangible.
so yes, i do think they are valid ways of thought. though, in reality finding the equilibrium price (as apposed to an equilibrium price) is nearly impossible to quantify to perfect accuracy.
further, your question ignores various market share/ types of competition or aka monopolies, oligopolies, perfectly competitive markets, variations of these, et cetera. each of which have a different basis for supply side price-setting, as well as demand side price-setting....
hope that helps somewhat.