Since I had the 970 until recently, I was struggling with VRAM constantly (it has 4 GB of VRAM, but only 3.5 is "fast" VRAM, the remanining 500MB is slower, but still faster than the system memory, especially when talking about DDR3, which I was also running until quite recently - and I would certainly hope the 666 MHz is meant to say 1600, because otherwise that's another big problem right there). Just going over the 3.5 limit meant a noticeable increase in various microstutters and lags, even if the framerate perhaps wasn't directly affected and seemed high enough. Setting the game so that it would need more than 4 GB would make things much worse in this regard. It wildly depended on the game, though - some games you would hardly notice it, some were heavily affected.
Sims tend to be affected quite a lot by this in my experience, and they're also easy to run out of VRAM due to the various high resolution liveries and all that (especially if you add custom liveries into the mix), and possibly also because, let's face it, they're not always perfectly optimized. RFactor 2 in particular is very VRAM hungry in my experience, but (as everything regarding performance in that game) it tends to vary greatly from one car/track combo to another. You can be running with barely 2GB of VRAM on one track with one car class, then load something like say the official Sebring with the two official GT3 packs, and suddenly you're at 4GB or more and you're really struggling to find settings to lower the VRAM usage below the 3.5 GB to keep the game from getting annoying microstutters (while still running seemingly fine framerates) without reducing the game to a blurry mess (and even that sometimes didn't really help).
This is one of the things racing sims once again tend to differ a lot from regular games (and one reason I wish they would be benchmarked a lot more in the media), as in regular games it seems a lot easier to not need as much VRAM and/or get away with them sometimes using the system RAM as a crutch to swap out some textures (I would certainly hope they're not using page file for that...just saying).
So yeah, that's why I immediately suggested VRAM when I saw stuttering issues mentioned with 4GB and 4k and supposedly OK framerates. It wasn't some random hypothetic suggestion on my part, it was experience. It was in fact also the primary reason why I upgraded my GPU - not because I was struggling with performance so much, but because I was regularly running out of VRAM in the worst moments possible and was getting annoying microstutters as a result. And the last thing you want in a sim during a race is random microstutters.