I don't think this would happen, the M16 would DRAMATICALLY change the battle tactics while a different sword type hardly does. The M16 holds 30 rounds, with it you can (ideally) take down 30 enemies in mere seconds, reload and do the same again while with a rifled musket of that era you get off about 3 shots / minute.
If the film was as historically inaccurate it would be all sorts of illogical.
I actually think the opposite will happen, with additional data and ever increasing quality in film making accuracy and quality will improve.
Of course it would, you are right. Here's the thing about swords: They came in many different designs, with different contexts behind their use.
Let's have a look at the sword used by Mel Gibson's William Wallace in Braveheart:
That is essentially a 16th century great sword. A sword that came about in a period of warfare that favored the use of the pike,
as seen here. Now there is some debate over whether the great sword was actually used to break up pike formations, it may have just been used by body guards. However, a sword of this length has different applications of use than a 13th century one-handed arming sword. The great sword was almost like a polearm, and it was typically carried on the shoulder during marching, not at the side as most swords were. (With the exception of the Romans, in most historical contexts swords were sidearms - back-up weapons) The point is, it does not belong in that time period, but people tend to overlook that, as the difference in time was "only" 300 years in a long ago period. Their perception of time got skewed.
The kilts and facial paint are from very different time periods as well.
There is a sword in existence that is reputed to be
THE William Wallace sword, this is the sword the filmmakers probably based their fantasy on, but it has a complicated history, and most likely did not look like it's current form in the 13th century. It has a 16th century hilt and a blade that has been skillfully forge-welded from three pieces of steel to make a longer blade. In other words, someone, or multiple people over time, took Wallace's sword (if it was indeed his sword) and forged a forgery.
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You brought up a good point about people starting to perform better research before they make a period piece, and I somewhat agree. However, there are still lots of willfully ignorant filmmakers out there, even with the advent of the internet. Not everyone is a Stanley Kubrick. There will always be directors that will drop accuracy in favor of convenience, or telling a better story. Many audiences like that approach, for better or worse. Tuco entering a gun shop and assembling a "super pistol" from different models of revolvers in
The Good, the Bad, and the Ugly doesn't make a lot of sense, but it's a great scene.
Sorry, got a bit carried away there.