Whenever you know you're going on holiday to somewhere do you always learn at least the basics? I do and I don't understand how some people can go to a country without knowing how to even say "Hello".
Well... some people just take a dictionary with their language and the translation of the language of the place they're going to (sorry if this sentence seems confusing). Others just try to stick with people who can speak their language.
I think it is worth at least learning the basics of that language as if nobody else can speak your language or translate between the two then you are stuck
I think it depends on what kind of holidays you like to go on and also where you're going.
Many people just want to relax somewhere in a hotel by the sea or something, cut off from everything else, in which case they probably don't need to learn anything (though "thank you" and maybe "hello" would still be nice).
I never was a fan of these kinds of holidays though. When I go some place, it's mainly for the culture. Museums, buildings etc., and most importantly: people. So if I don't know the language already, I do try to learn some common words and expressions at the very least as I think it's arrogant to expect all the locals with whom you might have or want to talk to know the language you're speaking.
I don't know how I'd feel if I was an English native speaker though. For me and many other people from non-English speaking countries, English is nevertheless the language we default to when traveling to places whose languages we don't know all that well, and I'm definitely more comfortable using English, a sort of neutral middle-ground, in those places than I would be using my mothertongue.
Well, when I travel somewhere, I use my phone as a English-to-(Language of where I am) dictionary. You should learn some basics of their language, you're the one going to their country. You need to know things like Hello, Thank you, Good-bye, Where is the restroom? etc.