My experience is exactly the opposite.
Trying to "take them alive" in 3e is a real decision with costs and benefits. If you go on hitting them lethally, there's always a chance you push them to -10 before anyone can keep them alive. If you want to hit nonlethal you usually take a penalty to hit, but you can attempt to subdue them by e.g. grappling and pinning. Many spells are useless, unless you come prepared.
I agree about the "perceived" costs and benefits, unfortunately they were not "dramatic" costs and benefits. It always became a metagame solution (can't take them below -10). Everytime I saw this tactic attempted in the game it involved no drama, only metagaming. Using the "subdual" damage rules ended up being a washout. The amount of times that the players missed their target trying to attack, almost always made the attempt futile. They would get frustrated, and simply revert back to doing regular damage. And if the solution was to go to the more complicated grappling and pinning rules then the entire point of the "drama" was lost in the minutiae of the rules. It also didn't work with things like dragons, which had such an outrageous grappling bonus that the players might as well have been trying to swim up a tornado.
The reason the 4e mechanics work better in the "dramatic space", in a narrativist way, is that they make it simple, without any need for metagaming. The players get to keep their concentration in the "drama" of the moment (capturing prisoners) rather than on how many more times they're going to miss, or if their grappling bonus is high enough (the metagame). There's no metagaming involved in the "drama" at that point.
The rules don't mechanically get in the way of the "drama", and they also don't make capturing prisoners a suboptimal choice within the mechanics. Because it is not automatically a suboptimal choice, it gets used quite frequently. The drama occurs because they are able to capture their opponents rather than kill them. It does not require a frustrating spiral of misses, or complicated grappling rules to do so. It can also be done with all manner of creatures, instead of only with those with a crappy grappling bonus.
With the 4e games I've run or played, and I've done a lot of that in the past 3 years, capturing prisoners happens all the time. And by ALL the time I mean once per adventure, or even more. I ran, and played 3.X games for a home group, and at conventions for almost 10 years. In that time I saw the "effective" capture of prisoners happen exactly twice.
So that dramatic opportunity was "supported" by the rules. It's just that it was done in a way that made the option not be used often, if at all.