Assuming "meaningless" truly is an apt description for them, I actually think this makes Tolstoy's stories seem all the more intriguing. Most violence and tragedy in life is meaningless, we humans ascribe meaning to it. It's sometimes fun to read a fictional piece and contemplate why the themes resonate with me, without having a ham-handed, prefabricated meaning shoved down my throat. Modernized fairy tales (and almost all modern fiction) are not intended to confront the consumer with these kinds of emotional/intellectual obstacles without a moralistic guide. This often makes it suitable for children, but I wonder if we underestimate children's ability to confront this kind of ambiguity (but that doesn't necessarily mean we should read Tolstoy's stories to them, or only ever offer ambiguity as a moral socialization strategy).
Meaningless violence is too easy, so is ham fisted moralizing. True classics find some kind of meaning, even in the meaninless tragedy of life, like the Iliad.
I grew up watching Disney-type stuff, and as I got older, it was off-putting to encounter stories that didn't seem to have a "point." A bunch of stuff happens and then you're required to just accept the utter lack of resolution. I know that some people view that lack of a resolution as "meaningless," and I'm not accusing you of that, but sometimes the lack of an obvious lesson is the lesson. People die, conflicts go unresolved, life goes on until it doesn't and sometimes all we can do is accept it.
Agreed, I think the secret is often a kind of subtlety that can often be confused with meaninglessness. For example, the first time I read "Of Mice and Men", I found the "meaningless" suffering to be infuriating - how could this book possibly be considered a classic? - until I later understood more context around the novel's time period and message, and realized it was only my juvenile tastes and expectations that made it seem meaningless (no happy ending? What is this tripe?)
I doubt Tolstoy wrote his stories without some kind of purpose, but I agree it would be a mistake to try too hard looking for meaning in case he just felt like writing up some sad shit.
The Iliad is an example of a classic with a bunch of meaningless suffering. But, the story is much deeper than 'bad stuff happens, the end' or 'bad stuff happens, that's just life'. I can write that kind of story all day, and I appeared deep to myself as a kid because I could 'see through' the meaning. At the end of the day, that sort of story is just boring. A real artist is the one who does get to some kind of coherent meaning to the whole thing. E.g. Iliad is a commentary on the Hellenist virtue ethic, and questioning why an ideally virtuous man like Hector is pulverized by a rage controlled tyrant like Achilles, without merely amounting to the juvenile 'virtue is meaningless' that passes as intellectualism these days. The same question is asked in the Psalms by the writer wondering at the fact that so many good people are oppressed and the wicked flourish. The Iliad began a conversation that echoes deep throughout history even to our present day. 'Bad stuff happens' just doesn't have that kind of staying power. People intuitively know there is more to our reality than that. That's why we are so bothered by sociopaths running our companies and governments. If 'bad stuff happens' is all there is to the story, then we would not be bothered.