Of course it's possible, but it all comes down to time, money and talent. There's an old saying in Hollywood (at least from a VFX friend of mine): "you can have it done right, you can have done fast, you can have done under budget. And you usually only two out of the three." On time and under budget is more important that accurate.
I know that alterations have to be made for the sake of budget, since that influenced what I could do when I worked backstage in musical theatre (usually on the properties crew, but I spent one show on the costume crew).
I had to explain to the director that even though the script for
Gypsy called for a monkey and a goldfish, we couldn't have either of them. She was clueless as to why, so I had to explain that I was pretty sure the nearest zoo would not let us have a monkey, and neither I nor my assistant had any intention of looking after a goldfish for 3 weeks. We had to make substitutions (ending up with a dog and rabbit).
The same director had to be told for
Peter Pan that no, we could not have a real fireworks-type bomb for Captain Hook to throw, because of safety issues (thankfully the fire department said no when I talked to them). I made a mockup with a styrofoam ball painted black and a string painted red. It worked fine. Ditto the safety concerns over arrows flying across the stage; one less-than-precisely aimed arrow and one person in the wrong place at the wrong time could be disastrous. We replaced the arrows with a line of dialogue.
Camelot was a different situation. I get why the armor was made of plastic; the actors and dancers were not trained in how to move in real armor. But at least when one of the breastplates came apart on stage, it was a much easier fix (done quickly during intermission; thank goodness for duct tape, staples, and glue guns; that thing held for the rest of the show's run).
And then there was the time in
The King and I when one of the priests asked me to fix his costume (I was doing props that year but he couldn't find anyone on the costume crew). I didn't have a sewing kit on me that night (I did after that), so I stapled his costume and told him to get one of the seamstresses to fix it ASAP because the staples would irritate his skin.
So improvisation happens. But I tried my hardest not to make it obvious to the audience that script changes had to happen, Lancelot's armor was fixed with anything I could grab during intermission, and an actor was stapled into his costume. Even the duct tape job on a broken goblet in
Jesus Christ Superstar held up to having liquid poured into it during the Last Supper scene (a stagehand broke it and we had no spare).
Now if we want to talk about historical accuracy... yikes. I'll forgive it if the show doesn't pretend to be accurate. For instance, Merlin eats a tomato sandwich? Fine. The show is entertaining and doesn't get pretentious about itself, so I don't care about tomatoes. I rolled my eyes over Morgana's clearly anachronistic modern dress, but to be honest, it's the guys who are the eye candy in that show.
I won't forgive
Reign, though. That show is an abomination that is only saved by Megan Follows. All else about it is utter crap.