I would also argue that learning vocabulary is backwards compatible with learning kanji and cross-compatible with learning other vocabulary.
As a few folks have mentioned, there are plenty of kanji that have many different translations in English (not to mention ones that simple don’t directly translate). For those kanji, I often find that learning them in a variety of different vocabulary words is what really teaches me what the kanji “means”. There may not be one direct English translation that encompasses it, but knowing half a dozen words that use it mean I still understand its “meaning”.
This is what I mean by “backwards compatible”: learning the vocabulary actually teaches me the kanji better than wanikani’s explanation could without context. It’s especially helpful for kanji that wanikani might just teach you as a suffix, like 的, or kanji like 不, which they teach as “not” but that you can see in 不眠症 (insomnia), 不同意 (disagree), 不正 (injustice), and about a thousand other words.
And by “sideways compatible”, I mean that learning a kanji in one vocabulary word can help you to learn other vocabulary words more quickly. I’ve had numerous conversations with co-workers where I ask them a question and the explanation will include something like this:
[After asking a coworker the word for “dehydration”]
Coworker: 脱水症状 (だっすいしょうじょう）
Me: Oh, wait, すい like 水？ (Verbally, “sui like mizu?”) And 熱中症の「しょう」?
Coworker: そうだ, and だっ from 脱する-
The English/Japanese swapping is just how our conversations tend to happen, with varying levels of English vs Japanese depending on my coworkers’ English skills and my Japanese vocabulary for a given topic
And this helps my brain remember it! Because I know 水 as water, but also 水族館（すいぞくかん）and 青水(あおみず）and a bunch of other words, just like I know that ‘hydro’ relates to water in English.
Same for 症, which I knew from 熱中症 and that I’m now learning in 不眠症, and so on and so forth. I’m not just memorizing it as “symptom”, the way wanikani teaches it, but with all the connotations of knowing it in different vocabulary words.
For me, at least, making this sort of web of connections in my brain helps me to remember new vocabulary, whether I’m learning it from a written form or talking about it aloud. And I’ve heard coworkers and students use this sort of structure (「kanji」from 「vocabulary」) to talk about the kanji that make up their names, so I think it feels like a pretty natural/intuitive way of connecting different meanings.
Obviously, it’s up to you what way of learning will work best: but personally, I don’t see any real benefit to skipping vocabulary, but I can see a lot of potential setbacks.