Since Putonghua is a standard English word, why do people use Mandarin for standard Chinese?
Why should they? People don't rely on dictionaries when they speak. “Putonghua” may be in dictionaries, but it is still not a commonly used word.
As for why “Mandarin” is used and not “Putonghua”, I believe that “Putonghua” was only recently included in English dictionaries. In China, 普通话 only became a commonly used term during the 20th century. (This is confirmed by Wikipedia.) So it seems likely that one reason “Putonghua”is not commonly used is that it hasn't had enough time to become adopted in English. I also think that another reason “Putonghua” isn't used much is because of phonetics: it doesn't sound like an English word, so people may find it hard to remember and to use.
It could be argued that it is more correct to use “Putonghua” rather than “Mandarin” when referring to standard Chinese. It is conceivable that changes in culture, geopolitics and education may lead to the term “Putonghua” eventually becoming the standard, commonly used term in English for “standard Chinese”. But I don't think it will happen soon. Not before at least a decade I think.
The majority of English speakers do not have much knowledge about the different Chinese languages.
Here are some comments on the usage of the terms Mandarin, Chinese and Putonghua.
Chinese: noun in common use in spoken English. It usually means standard Chinese, i.e. Putonghua. (口语)
Mandarin: noun also used by the general public, but seems a little more formal. (书面语)
Putonghua: not in common use. In general it is only used by someone with a little specialised knowledge of China and/or Chinese languages. Interestingly, in Wikipedia “Putonghua” is a &quot;redirect&quot; to the &quot;Standard Chinese&quot; entry. The article is well worth a look.