I don't seem to get linear style maps very often. I seem to find my biggest war threats will either 1) land on me with a naval invasion of garbage (mostly an annoying hindrance rather than a real threat, as nationhood once you figure the WHEOOHRN is you is generally fine even with muskets vs that) or 2) move through AI territory that won't cancel deals.
But that's a subset already. In most games where I'm gunning culture I am not the first target for any AI, while a DP would get me involved in a war (I do a lot of things to abuse diplo). In some of the exceptions, the AI would still have a stack in my borders hampering me on DoW and I'd have to deal with it.
If diplo looks bad one doesn't *have* to go culture. Even the cathedrals/religion approach has until liberalism to decide (though you might invest in inefficient infra to an extent), and you can usually sort things out by then and switch to a rifle war or something.
I definitely use them when they'll help though.