I would be interested in both; the historically accurate vs the "alternative history" or "general past" setting. I'd also suggest there is a spectrum; at least I see it that way in my own writing.
In both cases, the advantages and disadvantages arise from constraints. Or as you said, "limitations."
Is it possible for historical correctness to detract from the setting,
I think, to be more accurate, it could make the setting both richer and more coherent or consistent. But it can certainly detract from the plot, and alienate some readers, particularly female readers, LGBT readers, etc. The medieval past was over-the-top sexist; not in every culture but most of them. The Old Testament, read literally with an eye toward the treatment of women and children, is a good starting point. The same for strict Islamic codes; these guys were not kidding around; women were property and did what they were told or they were beaten. A man raping his wife or female slaves was expected. There are instructions there for how to sell your daughters, etc. The vast majority of marriages were arranged, by men for the women they controlled, for financial, political or social reasons: Effectively sex slaves traded by their owners for personal advantage. Children were likewise treated as slave labor.
I think most fantasy readers prefer a less dark world for more than half its population, and want some notion of Romantic Love, self-agency, and other modern social interactions.
Accurately portraying the technology is one thing; accurately portraying the culture is another. I could certainly appreciate an accurate portrayal of the technology; that would be informative, and the constraints on the characters make it a bit more difficult for the author, but to my mind in a good way, there are no free deus ex machinas to get the author out of a plot jam, or solve a character problem quickly. (Maybe that's the job of magic.)
Accurately portraying the culture is a different thing. Fiction needs to be relatable to the reader, and modern notions of family, marriage, sex, love, religion, sanitation and other cultural phenomenon are far too different than what was commonly true in medieval times. To me, those constraints would prevent the vast majority of readers, including me, from relating to or enjoying a story; I think the attitudes are too alien.
The disadvantages of the mash-up.
The big disadvantage here is the risk of incoherency. As you suspect, various inventions and cultural innovations have ramifications and consequences. Introducing an invention from the 1600's to solve a writing or plot problem in the 1200's may ignore a dramatic shift in cultural or scientific knowledge that the invention to easily solve a writing problem can ring false if the other ramifications of that invention are not realized in the story as well. If the reader knows them.
However, this is not always the case: Ulfbherht Viking swords from the ninth century are an example. From that link:
Dozens of these swords — made with metal so strong and pure it’s baffling how any sword maker of that time could have accomplished it — have been found in Europe, along with some knock-offs. They are all marked with the Ulfberht name and two crosses, though some of the imitations are missing a letter here or there. [...] At the time the Ulfberht swords were forged (approximately 800–1000 A.D.), equally perplexing swords made of a substance called Damascus steel were being produced in the Middle East out of a raw material, known as Wootz steel, from Asia. Both Damascus steel and the Ulfbehrt’s so-called “crucible steel” had high amounts of carbon. [...] It was thought, before Ulfberht was discovered, that the capability to remove slag to such a degree only became possible during the Industrial Revolution. Iron ore must be heated to 3,000 degrees Fahrenheit to accomplish this, a feat the Ulfberht makers apparently accomplished 800 years ahead of their time.
Thus, I'd posit that mixing might not be that bad, steel to rival our own modern steel was being made and used 1200 years ago, but did not result in an industrial revolution, new architecture like skyscrapers, vast machinery, etc. The only artifacts left using it were swords. Perhaps other modern ideas can be introduced and what seem like "obvious" ramifications can be ignored, for cultural or religious or economic reasons: Perhaps Ulfberht steel was too expensive to use for anything other than a sword: The strength of that steel made it light, fast, magically flexible and difficult to snap, and so hard it could cut a man in half and still hold a razor edge. Perhaps the failure of imagination is not considering these properties separately, thus not imagining any other use (like machinery, architecture or shipbuilding) that would not demand all of these properties.
I think the advantages of the mash up (including the lack of scholarship demanded) must clearly outweigh any value of accuracy. Its why we invent our own worlds and maps, and give our medieval peasants cultures not too realistic for their time, so our readers can relate.
I always go for that option; I prefer to invent my own constraints and culture, and even if the setting is medieval or even more ancient, I invent the constraints within that setting too. I've done the same in modern times: Put my characters in a town I invented with politics, landmarks, facilities and what not of my own invention.
Consider (as I do) your setting as almost like a character you invent. It presents both opportunity and obstacles. e.g. a private place where teen lovers might meet is easily found. Food and water are easily found next door. The local university has an expert in what you need. OR, the place where action X must be accomplished is two hundred miles away. The town where your father took a job is extremely homophobic. You have to go to a school three steps down from your previous awesome school, that bores you to tears and has effectively robbed you of two good years of education, and apparently everybody in it loves country music that you despise and considers the music you like literally evil and blasphemous.
I invent my setting like I invent my characters, and would not use a realistic setting just like I would not try to invent a character matching all we know about a historical figure. While many readers might like a fictional but accurate adventure of, say, a twenty-year-old Thomas Jefferson, I couldn't write it.