"The canon" as most people would recite... Moby Dick, Crime and Punishment, etc.... is now at least 60 years old, if not 100. It's a fuzzy thing, but it's certainly old.
Merely being old is not a problem. Great literature is perhaps not literally "timeless", but it can survive being pulled out of its original context, and to the extent that students have to engage with a foreign context, that can be part of the point.
However, that's 60-100 years of language shift since the canon was canonized, and that is a problem. Not necessarily insurmountable, but it's one that needs to be taken into account. I don't see anyone taking it into account, because if anyone questions the canon, they are obviously just a drooling arm-dragging uncultured buffoon who should be evicted from sophisticated society.
But, you know, I'm in my mid-40s, and I've seen real, bona-fide language shifts in American English. Even the English of the 1980s is getting dated. Reading back into the 1950s will result in readers encountering a number of dead words. I remember reading in that era, and every celebrity seemed to be described as "indefatigable". One can assemble from the roots a good guess about what it probably means, and in this case, such a guess is correct, but you can't actually be sure without looking it up or reading it in a lot of contexts. When's the last time you saw an actor described as "indefatigable"?
It doesn't take many of these sorts of things before you are unable to analyze, enjoy, or even necessarily comprehend the "great literature" because you're too busy just figuring what on Earth it is actually saying. It's hard to analyze subtext when you're a normal reader struggling to grasp the text.
Of course, I say this into a culture that is still holding up the original Shakespeare as the sine qua non of Literature, despite the fact it is now over a century past the point that a "normal person" ought to be expected to comprehend it on a base level. If someone wants to teach Shakespeare to a modern teenager, it ought to be done in translation at this point. That I wouldn't mind; there's still a lot of "literature" in it that could be studied through a translation. But the idea that a teenager should be expected to read
For who would bear the whips and scorns of time,
The oppressor’s wrong, the proud man’s contumely,
The pangs of dispriz’d love, the law’s delay,
The insolence of office, and the spurns
That patient merit of the unworthy takes,
When he himself might his quietus make
With a bare bodkin?
and get anything out of it is just insane. At least 4 lines have a
major vocabulary issue, more depending on what you expect from your teen. All the rest have at least minor issues, using words that are at least unusual in modern English, and many of them with connotations that are even more unusual if not dead.
But 18th century literature is starting to read similarly to a modern teen, and 19th is a bigger stretch now than it was when I was young. It is not wrong to account for this in trying to figure out how to reach modern students, it's just realism.