Whereas computing the portfolio standard deviation is computationally straightforward, there is no easy way of doing so for the semivariance. WHY???

I think they’re referring to the fact that you have to 1) count the number of negative deviations (i.e. when x-mean(x)<0 ) 2) sum the squares of negative deviations I’d agree that computers these days make the brute-force method of getting these calculations easier. But it is harder to do algebraic manipulations to get semivariance and estimations of semivariance, which is probably where this comment is coming from.