How does R's aov function 'work better' with orthogonal contrasts?

The help page for R's aov function states:

The default ‘contrasts’ in R are not orthogonal contrasts, and aov and its helper functions will work better with such contrasts: see the examples for how to select these.

What does 'work better' mean in this context? My recollection is that the anova table's F statistics are invariant to changes in contrast coding, but maybe I'm mistaken.

Here is an example that shows that the default contrasts and orthogonal contrasts yield the same anova table:

Example table with orthogonal contrasts:

> op <- options(contrasts = c("contr.helmert", "contr.poly"))
> summary(npk1 <- aov(yield ~ block + N*P*K, npk) )
Df Sum Sq Mean Sq F value  Pr(>F)
block        5  343.3   68.66   4.447 0.01594 *
N            1  189.3  189.28  12.259 0.00437 **
P            1    8.4    8.40   0.544 0.47490
K            1   95.2   95.20   6.166 0.02880 *
N:P          1   21.3   21.28   1.378 0.26317
N:K          1   33.1   33.14   2.146 0.16865
P:K          1    0.5    0.48   0.031 0.86275
Residuals   12  185.3   15.44


Same table with non-orthogonal contrasts:

> op <- options(contrasts = c("contr.treatment", "contr.poly"))
> summary( npk2 <- aov(yield ~ block + N*P*K, npk) )
Df Sum Sq Mean Sq F value  Pr(>F)
block        5  343.3   68.66   4.447 0.01594 *
N            1  189.3  189.28  12.259 0.00437 **
P            1    8.4    8.40   0.544 0.47490
K            1   95.2   95.20   6.166 0.02880 *
N:P          1   21.3   21.28   1.378 0.26317
N:K          1   33.1   33.13   2.146 0.16865
P:K          1    0.5    0.48   0.031 0.86275
Residuals   12  185.3   15.44


Is this just about ease of numerical computation?