Somewhat humorously, you’ll actually learn quite a few hiragana words in your time on WK in the form of kanji. A very large number of hiragana words actually used kanji long ago, but, for various reasons, stopped. Some of these words are contained in the vocabulary for WK, so keep an eye out for vocabulary descriptions. It usually tells you when a a jukugo you’re learning is not utilized much (Jisho will also say in grey text usually if something is usually written in kana).
Talking with Japanese people through a text medium and/or reading Japanese literature (manga included) are definitely the best ways to pick up kana words, especially katakana. Unfortunately, as @xBl4ck mentioned, grammar is going to be necessary to accomplish either of these with any measure of comfort and/or sanity.
Start learning grammar as quickly as you can then start trying to read simple resources (NHK Easy, wikipedia articles of topics you know very well, etc). The farther you go from colloquial Japanese (like high literature), the fewer hiragana and katakana words you’ll see. From my experience, the Japanese like to skip using kanji in a great number of verbs, especially those that are frequently used and utilize only one or two kanji normally (来る and 行く are great examples). Of course, する verbs and those with a large number of homophones usually are used with kanji.