I agree with the suggestion that a lot of Faye's earlier behaviour - particularly the violent outbursts - should be treated as very loosely canon, or kind of glossed over as Early Installment Weirdness, with Jeph still figuring things out as far as tone and whatnot. I think it's best to look at those early strips as broad strokes in canon; after all, several of them definitely refer to AnthroPCs as being property with explicit references to having owners and curfews, and needing permission to go out by themselves (or be taken somewhere). I'd say that's been retconned with the "AI companions" backstory that has since been revealed.
However, we still do see examples of Faye going a bit too far with her abrasiveness towards other people.
In this strip from just a couple of years ago, Claire admittedly puts her foot in her mouth somewhat with her remark, which Faye probably would've taken better had it been said by a closer friend (then again, maybe not). For daring to point something out to Faye and being a bit incredulous and scornful of her completely overlooking the obvious,
she is threatened with violence unless she keeps balancing a can of beer on her head.
Typing it out like that, it does seem a bit silly and minor, and it was obviously played for laughs. Still, we have a punchline that's based on Faye threatening violence and being intimidating over a pretty minor gaffe on Claire's part, where she did kind of have a point. That's coming within the last couple of years, so we do still see that element of her character in firmly established canon, at least to some degree.
To that end, it's understandable that some readers don't find her particularly likeable or sympathetic, and that characters within the QC universe have their issues with her, or in Dora's case, are at the end of their rope as far as she's concerned. She's not a complete monster, but she's a lot to take, and she can be very difficult and abrasive. On top of that, while she'll readily call out other people on their BS - rightfully so, in many cases - she kind of has to be handled with kid gloves herself. To a certain extent, there's a sense of her being able to sass, insult, threaten, intimidate, or even hit anyone she pleases, but people shouldn't dare criticise her.
As for where the story is going, I wonder if we're going to see a bit more of her family. I think it'd be interesting to bring them in again (as well as Dr Corrine) and explore some of those issues and her backstory again. A lot of good theories have been put forth about David Whitaker, and I think it'd be interesting if the comic does revisit his suicide and the possibility that he was an alcoholic. I don't think Faye's being written out, I think she's being set up for a new character arc.