alt Hacker NewsGreat quote!
Your final sentence seems a bit odd in that context though: Churchill's point is that Latin and Greek actually isn't useful at all, so it would follow that it isn't better to do both (i.e. study the classics as well as English), especially as time to learn them would have a huge opportunity cost, e.g. you could use that time to study more English composition instead.
(If you think they're worth learning just for their own sake then that's another matter, but the quote seems to imply that Churchill wouldn't agree.)
I think Churchill's main point is that they neglected teaching English well. However, if you read him and politicians of the era, you will find plenty of classical references. If we dig into classical history it is quite amazing how many of the same things we see. I was reading something about how certain cities in Asia Minor (modern Turkey) were spending more and more money on civic vanity projects and having to be bailed out by central government in Rome. Very similar to patterns today.