Can't remember who wrote it - my Latin is far in the past! - but there's a cheeky poem, possibly by Catullus, about someone from the provinces who caused amusement in Rome by pronouncing the H in, for instance, the Hadriatic Sea!
What's going on in modern US English? Is it only herb that turns into erb, or are other words starting with H doing the same? I seem to have heard others on CNN, but can't be sure.