So in 4.4 we are introduced to ninki and the lesson likens the usage to kirei with:
totemo ninki as very popular and totemo kirei as very beautiful.
When I learned this originally, I could swear I learned that despite the way we use popular in English, it was different in Japanese. Kirei is an adjective which is why sentences end with desu, because it is or it is not... but ninki was not an adjective; it was something that was quantifiable in that you have it or you don't, which is why sentences end in ga aru / ga nai
Because of this explanation, I learned that to express someone was very popular, you should say, "takusan ninki ga arimasu" versus "totemo ninki ga arimasu" or has a lot of popularity vs has very popularity.
Are both correct? Is this something which changed colloquially in the last 20 years?

こんにちは (Konnichiwa) azenphish,

Thank you for your question!

にんき (Ninki) is a tricky word! It's a noun that can sometimes act like an adjective. You can translate it as "popularity," but depending on the context, it can also mean "popular." 

You can use にんき (ninki) with either です (desu) or が　あります (ga arimasu).

Since it is a noun, you can use it with が　あります (ga arimasu) to say you "have popularity": ie: "are popular." 

• かれ　は　とても　にんき　が　あります。 (Kare wa totemo ninki ga arimasu) "He has lots of popularity. / He (is) very popular."

However,  you can also use it with です (desu). です (Desu) is a polite sentence ender and can be used with い (i) adjectives, な (na) adjectives (like きれい kirei) AND nouns (like にんき ninki). 

• かれ　は　とても　にんき　です。 (Kare wa totemo ninki desu.) "He is very popular."

You can use にんき　が　あります (ninki ga arimasu) and にんき　です (ninki desu) interchangeably; howeve r, にんき　が　あります (ninki ga arimasu) is more common in written language, whereas にんき　です (ninki desu) is more common in spoken language.

To say someone is very popular, you can use either たくさん　にんき　が　あります (takusan ninki ga arimasu) or とても　にんき　が　あります (totemo ninki ga arimasu). Both are perfectly correct! 

とても (Totemo) is an adverb that describes adjectives, verbs or other adverbs. You are correct in saying that it would sound strange to use とても (totemo) with a noun; however, にんき (ninki) is a little special! Since it can sometimes act like an adjective, we can use it with とても (totemo) here. 

I hope this helped! Please let me know if you have any other questions.

べんきょう　を　がんばって　ください！(Benkyō o ganbatte kudasai!)