CaS =/= railroad. Strategy allows you to pick different fights (and under different conditions). It doesn't (in CaS) generally allow you to win those fights without fighting. Unless you talk your way out of them, of course.
Most of the time IMX, CaW devolves into finding loopholes and playing the DM, not actually playing the game. It's completely independent of the characters and only depends on the players...like chess. Which is not how I like to roleplay.
Basically, the strategy involved in CaS[1] is about getting the DM to create encounters that are favorable to the play-style you have/want, rather than avoiding fights entirely. Because there's a wide range of "CR appropriate" fights. And CR is such a rough measure that you can bend quite a ways. And no one holds strictly to the "all fights are exactly balanced" extreme.
For example, take one of the 5e published modules (Princes of the Apocalypse). These are all as CaS as things get. But in one section, you could fight your way up a certain tower room by room (facing a bunch of penny-packet fights). Or you could do what we did, which was parley our way up to the top, then fight everything all at once. That "strategy" produced a very different set of fights than the other option. Heck, we went and did the same sort of thing (rush into the middle and blow them all up at once) in another part of the module, where you could have lured out and defeated them in detail.
[1] I hate these terms, because as used they're basically pejoratives. CaS == you guys don't want to think. CaW == we're so smart and "realistic". When in reality, the DM only doesn't win because he chooses not to. Neither is "fair" or "earned"--the DM is always building things that can be defeated. Because otherwise you get rolled at level 1 and TPKd, because the DM holds all the cards.