Part of it is just my preference for having things be very specifically grounded in a place and time. Whether it's explicitly stated, or at all plot-relevant or not, I like knowing what state the Winchesters are in, where the motel is, what the weather's like--generally only to the point that it would actually matter to them, in casual observational ways (i.e. Sam being kind of annoyed by a draft for a half-second, vs. Sam pontificating at length about this draft and the history of the town they're in for 1000 words--I seriously doubt new places or transient states of being are ALL THAT NOVEL OR INTERESTING TO THEM, XD). Same with canon referents and signposts, even if (especially if?) these things don't directly factor in to the main drive of the fic. Since a lot of fan fic's intention is to provide some sort of connective tissue--be it emotional, narrative, or simply this-is-how-we-even-got-from-New-York-to-O
The other part of it is, if you put in your author's notes "this story can take place any time" you're basically saying that in the last nine years--or however long it's been, for whatever canon--there has been no character development whatsoever, and nothing has happened, or nothing that happened mattered a whit.
There are storytelling modes where this is intentionally true. But dollars to doughnuts, your beloved movie, TV show, book series, or comic is not using one. Unless your fandom is Family Circus, in which case, carry on.
This really shouldn't be news to anyone at all, and I don't think anyone would really want to argue "Dean is the same person in S1 as he is in S9!" or hell, even "Kevin is the same person in 9x02 as he is in 9x09" (though I'm sure there are plenty who would argue that they SHOULD be, and plenty who are annoyed because they aren't and this plenty has no idea what to do with this information, heaven forbid accept it, XP --sorry, wanky). But I also don't think it gets talked about or considered in proportion to its expansive range and depth of effect.
I think that setting something in this season or that one makes a huge difference in not only who they are as a person--their core or whatever--but also just how they come across on a day-to-day basis, how they pattern their thoughts, what they notice, what's important, who's relevant, whether their toilet paper rolls over or under... And while the big macro things obviously make a huge difference in x or y, I think a lot of it has to do with tiny micro ones that you can't even really articulate. That's why this matters (well, to me, in any case) even in fluffy cuddlefests and PWPs. I think it changes how someone just walks into a room, so I think it totally changes the vibe of anything else the character chooses to do in said room! Or in the doorway or said room, or you know. Whatever. :P
What's your take?
When I sit down to write or read, the first thing I want to figure out is when the scene is, because for me that's the #1 to "So, who are you?"
Sometimes I'll read something I've written and think, huh, that's kind of weirdly S7 Dean, not S8 Dean. Either I need to pick this up and put it somewhere in S8, or rewrite that. gdi. XD
And like, last night I read a really great fic that I will probably rec here, but for the life of me I could NOT figure out when it was supposed to take place. The entire time I'd tentatively been guessing S2, but at some point there was a reference to the Wall of Sam in late S6 and I was just like lolll good lord are you serious? I adore the fic for reasons separate from the Winchesters' characterizations, but let me tell you, I'm pretty sure I'm still not over how stunned I was to figure that out!