How important is fluff to you? Do you base an army around the fluff and make the looks/minis suit the background you have for them or is it the other way around? Do you use units that would never fight alongside one another fluffwise? Do you care for the fluff or is it all about the rules for you? Do you write fluff for your armies?
I'll chime in late, and this is going to have to be shorter than I'd normally prefer, since I'm stuck in a few other projects at the moment that require my attention so I hope that you'll forgive me. I'm a tabletop RPG player at heart, started out with D&D in my pre-teens, spent my youth on the Baldur's Gate games, and even wrote my dissertation on games and fan fiction, so in short: yes, the fluff is important to me. I can't help but immerse myself, no matter if it's around the table with my friends, across the table with my plastic soldiers, or writing "Greetings friend" among a sea of "lol hi gold plz" in a MMO-game. It's who I am. Of course, if you're going to be playing greenskins, you better do it for other reasons than to win every single game.
However, we have to remember that it's still a game that's supposed be competitive, and if you're looking for a purely fictional experience, there are better mediums available. I believe a healthy balance of the two (rules vs. fluff) is the way to go. Whenever I write an army list, I always have a bit of fiction in my head about how that army came together. I'll let it guide my decisions but I won't be too strict about it. For example, Night Goblins are mountain living creatures while Savage Orcs usually live in the Southlands, so normally it'd be hard for them to fight together. Well, if I add a Black Orc Warboss as the general, it can be a long running Waaaagh!'s that has been going for many months and miles, where different tribes have joined up as they went. On the other hand, a popular tactic is to have your Black Orc Warboss lead a large unit of Night Goblins, to provide the static combat res while protecting the general with their nets. But I just can't bring myself to put the big guy in there, that'd be one miserable Warboss that only got to beat around Night Goblins. So there are limits to what I'd field, but I leave myself a lot of leeway. Again, because it's a game and I won't have as much fun playing it if I field awful lists because I limited myself too much.
What I would like to see is for the designers to push the fiction more, like they used to do in the previous version. I loved the idea of a Badlands Nomadic Waaagh! where boar boyz were moved to Core, but you couldn't field any war machines or infantry. Or a Mountain Waaagh! where Big Bosses (heroes) could ride on Wyverns, Squigs were Core, but you couldn't field anything mounted, no chariots or anything. I saw a couple of nice suggestions in the old Dwarf book as well, with an Underground Assault army fielding Miners and Ironbreakers as Core, but Warriors, Longbeards were Specials and the only warmachine available was the Organ Gun as Rare. It probably can't be done on an official level because there's just not time enough to play-test it all. But it should be included as an option for friendly garage games.
Another idea, which we see a bit of in the older books currently out, would be to let the General impact your army restrictions, such as the Tomb King making Light Chariots a Core choice, or a Dwarf Lord allowing an extra unit of Longbeards. It would be interesting if, say a Black Orc general made Black Orcs a Core instead of a Special Choice, while a Savage Orc general made the Boar Chariots frenzied, but made Squig Hoppers rare, or even not allowed. Similarly, a Night Goblin general would make Orcs move from Core to a Rare choice, while Black Orcs could not be fielded at all (they would never allow a weedy goblin to lead them).
In the end, fiction is great and adds a lot to the hobby, but it needs to be supported gaming wise before you can go all out on it. As it stands now, it is not, which means any theme or fluff limitations we place on ourselves will have to be anchored in what can actually work gaming wise. Running a 'Ard Boyz list with nothing but Orcs and Black Orcs, no goblins allowed except if they're properly whipped war machine crew (by an orc bully) can definitely work, you're setting out some limitations but still have enough to play around with. But if you were to go All Night Goblin (like those supposedly epic underground battles against the Dwarfs), refusing all fast cavalry, chariots and war machines (since they're common goblins and not night goblins), with a Lord leadership of 7, you're setting yourself up for a face smash. It might be very fluffy, but it's so uncompetitive that it probably won't be any fun to play with at all. Then you're probably better of reading a Gotrek and Felix novel for that extra dose of fluff.