I'm not completely certain what you mean by vanilla in the context.
I'm borrowing the term from Ron Edwards (or, at least, my take on his use of it). I mean "without fancy bells and whistles".
By "narrativism" I mean play in which the goal of play is "story now" - ie play that will generate a story that is aesthetically satisfying for the participants, without any single participant having to take responsibility for generating such a story.
By "vanilla narrativism" I mean play that aims at, and achieves, this narrativist goal without using fancy mechanical devices to do so. Examples of such devices include relationships in HeroWars/Quest; the somewhat analagous spiritual attributes in The Riddle of Steel; beliefs, instincts, some traits, and the artha mechanics that these feed into in Burning Wheel; etc.
The point of these sorts of mechanics - or, at least, one point of them - is to deliberately and self-consciously focus the participants in the game on the aesthetic/thematic priorities for play.
Now in fact it's probably not true to say that 4e, as I GM it, is completely vanilla, because my group does use various of the mechanics - some powers, paragon paths, etc - to focus our play of the game on our aesthetic/thematic priorities. But one feature of 4e is that it tends to imbed these features of the game within more traditional overall mechanical elements. The metagame character of powers, for example, is to some extent concealed because these look just like traditional components of lists of class abilities. And paragon paths occupy some of the same functional space as the traditional choice of character class.
So maybe I should say that [/I]4e is vanilla relative to the received habits of traditional and mainstream fantasy RPGing[/i]. But precisely because it is vanilla, because it doesn't have mechanics that lead you willy-nilly and irresistably into story now, it is - at least in principle - in danger of getting nudged onto other priorities.
There is NO DOUBT that the concerns you address can and do happen. But a good DM and players dedicated to being involved in a great story can easily and instantly avoid those pitfalls without needing to sacrifice the depth of the mechanics.
The extent to which this is feasible for a group, relative to its goals for play, is so variable across the range of actual and possible mechanical systems, and the range of actual and possible group preferences, habits, etc, that I doubt that very much meaningful generalisation is possible.
Speaking from my own experience: systems that require the participants in the game to actively ignore elements of them (for example, to suspend the action resolution rules in order to bring a scene to a conclusion) will tend to fail one of my desiderata for play, namely, that the game should produce an aesthetically satisfying story
without any of the participants having to take responsibility for that. I want the players to be able to play their PCs to the hilt; and I want to be able to frame my situations to push the PCs and their players; without anyone having to keep in mind meta-level concerns about where the action resolution mechanics might tend to lead us off the rails.
Others undoubtedly have different priorities, different experiences, different cognitive and aesthetic inclinations, etc, etc.
I would also add - I think the notion of "depth" as you use it is not one that is necessarily capable of generalisation. What one player experiences as "depth", another may experience as "needless distraction." A range of different examples is possible. Rolemaster, for example, has rules for generation of PC hand, head and foot size, which are then meant to factor into questions about the size and suitability of discovered magical loot. For some players of a fantasy RPG, this will produce an experience of depth. For others, it will produce an experience of irritation. (For yet others, they might respond differently dependnig on mood, desires for a particular play episode, the way it fits into other aspects of the system, etc.)
AD&D "solves" the issue of one-size-fits-all by specifying that magical clothing magically resizes itself. (A bit like the notorious "unstable molecules" of Marvel super hero outfits.) For some players this adds depth - there is now an explanation, in the fiction, of why clothing size is not an issue. For other players - and I would probably be one of them - the AD&D explanation doesn't add depth so much as a minor piece of silliness. I would rather gloss over the issue, or handle it a compeletely different way (magical items are primarily gifts from patrons, for example, and therefore selected in part on the basis that they fit the recipient), then have magical auto-resizing as a default part of my fantasy world.
This is also yet another example of how features of a system can get in the way of narrativist (or other forms of) play. Every minute spent at the table worrying about whether recovered loot can fit the PCs who want to wear it is a minute not spent engaged in play that will generate a story that is aesthetically pleasing for the participants (at least if the participants include me).