This is just the observed variance. Which means that you assume that this will be the variance in the future.

Don’t make decisions for evolving systems based on statistics.

Insider info on the other hand works much better.

This is why Markowitz isn't used much in the industry, at least not in a plug-and-play fashion. Empirical volatility, and the variance -covariance matrix more generally speaking, is a useful descriptive statistic, but the matrix has high sampling variance, which means Markowitz is garbage in garbage out. Unlike in other fields, you can't just make/collect more data to reduce the sampling variance of the inputs. So you want to regularize the inputs or have some kind of hybrid approach that has a discretionary overlay.

That's the first thing I thought of. I read the opening of this article and thought "oh this could be applied to a load balancing problem" but it immediately becomes obvious that you can't assume the variance is going to be uniform over time

Upvoting b/c this comment is true, obviously I disapprove of insider trading.

Volatility is fairly predictable. Or at least much more predictable than returns

Doesn't it make more sense to measure and minimize the variance of the underlying cash flows of the companies one is investing in, rather than the prices?

Price variance is a noisy statistic not based on any underlying data about a company, especially if we believe that stock prices are truly random.