I'm not sure when the 'sympathetic character' became a necessity for modern authors. Certainly the Brontës didn't feel constantly pressured to write sympathetic characters, or they'd never have got away with Mr. Rochester (a bigamist bully with an ex-wife locked away in the attic) or Heathcliff (basically a stalker, albeit a very charismatic one), and we have to acknowledge that Becky Sharp would never have been created if Thackeray had had to make her sympathetic with redeemable qualities at the end.
I say this with an awareness that the protagonist of my latest novel, "Theodora: Actress, Empress, Whore" has been seen as unsympathetic by some. Of course, sympathy is in the eye of the beholder, so while some readers have found her cold, or even ruthless, others have found her funny, smart, passionate, as well as ambitious. Not surprisingly, I'm with the latter group. (I'm also grateful that, so far at least, the latter group is larger!)
I guess our viewpoint depends on what we want of our characters, and - most especially in this case - if we want an attempt at truth from our historical fiction or if we want the kind of dramatic arc that Hollywood so specializes in these days - the narrative where everyone learns from their mistakes, and everyone becomes a better person by the end. Except for those who can't or won't change - they die. Obviously.
Personally, I'd rather read - and write - characters that are closer to reality, than those that conform to the protagonist-must-always-be-lovely narrative that has been thrust on us all. I'm fine with the fairy tale in its place, but I'm not sure that should be the pattern for every, or even most, novels. Most lives are not fairy tales. Most lives do not conform to a three-act structure, or a 12-point hero's journey. And in "Theodora," I've tried to write what I know to be truths - that a woman who has been prostituted may well find herself disassociating from her world, from society. That a woman who rises from nothing to great success, loses it all, and then rises again to enormous power, may well find that power corrupts and absolute power corrupts absolutely. That actually she is more interesting for being flawed and not always likeable, not less. That not every 'feisty' (oh, how over-used is that word!) heroine also has a heart of gold. That someone can take charge of their own life, turn their destiny into mission and, in doing so, they might become more admirable, but possibly less lovable.
This likability-imperative really interests me, not least because I suspect there's a degree of sexism at the root of it. Powerful men litter our fiction and yet we excuse their faults, their rudeness, their 'Mr Darcy arrogance,' because they are powerful. (Or could it be because they are men?!) But woe betide the strong, powerful woman character - it's her duty to see the error of her ways (Elizabeth Bennett), to repent ("The Taming of the Shrew"), or she is sent off as ignominiously as the beautifully coiffed, elegantly clothed but ultimately unloved Baroness ("The Sound of Music"). It also feels very modern. The fabulous 'women's movies' of the 30s and 40s didn't always have likable women protagonists; they had brilliant, strong, sharp-tongued, smart-mouthed, passionate women. From Stella Dallas to Scarlett O'Hara to Mildred Pierce, the point wasn't to be liked, but to be interesting.
And yes, fair enough, we do want our characters, men and women, to have some warmth, however hidden; that's why having Marilyn Monroe play a gold-digger in "Gentlemen Prefer Blondes" was so successful - she might be after your money, but it's Marilyn who's after your money. (Diamond-hungry, yes, but look at the vulnerability!) That said, I'd trade niceness for passion and strength any day, especially in historical fiction - not least because I think it's far more likely to be true to the essence of the actual person. How rare is the absolutely likable tycoon? The lovable king?
Ultimately, I guess it depends on who you want to sit beside at dinner; they might not be easy company, and you might have to work hard to keep up, to get a word in edgeways, but I'll take Theodora, Margot Channing, or Tracy Lord over Snow White and Cinderella any day. I like my heroines with bite.