I can say that learning the kunyomi and onyomi readings are EXTREMELY useful. It may not feel that way at first, but learning those is an investment that pays off tons later on.
There's other reasons, but here's the main one. If you're really trying to get good at Japanese, you're going to reach a point (sooner than you think) where you start to see words you've never seen before, but can figure out the meaning and reading just by looking at the kanji characters. This makes acquisition of new words SO much easier, and cuts down dramatically on your studying.
A really simple example is 新 (definition: new. readings: あたら.しい, しん). You quickly learn that readings that have stuff that come after the kanji (like あたらしい > 新しい) are rarely used in kanji compounds, so for this one, you know that if it appears in a word, it's probably going to be しん. So when I started working at a high school in Japan and saw the word 新学期 (しんがっき), I was able to piece together the readings I had studied (the first two kanji you learn pretty quickly, the last one is a bit harder) and pick it up without looking up anything.
There's one more reason that I love, but you're going to have to take my word for it, because it sounds pretty far-fetched for someone without a strong kanji background (as we all are in the beginning). Kanji readings actually help with *listening* comprehension. Really! Let's go back to the 新学期 (new semester) example.
When you are listening to Japanese, there are no kanji, right? If you could literally see the sounds coming out of someone's mouth, it would be the hiragana only. However, you have the context of the situation to guide you. So, let's say someone says this:
You: 運動会（うんどうかい）はいつですか？ (When is the sports festival)
What is "B" going to answer with. A date or time, most likely, right? So your brain starts thinking of time related words, even though you don't explicitly tell it to. Since you're in a school environment, your brain is also keeping school/education stuff ready.
B: しんがっきがはじまったらすぐですね。
So you hear this, and you can hear the が はじまったら すぐ です ね, part, but the しんがっき thing is new to you. However, when you have those kanji readings in your head, they start to pop out as you hear things.
So the しんがっき changes into..
1. 新 (you just assume しん means 新 because it is the most common kanji for that reading)
2. がっ（がく？？）since you're at school, your brain is probably going to throw out 学（がく）at you.
3. き...well, if you're talking about time, 期 is a commonly used kanji (since you already studied and know the meaning)
So you can hear a new word and your brain puts the puzzle pieces together for you.
I have no doubt this seems somewhat impossible, and I didn't personally realize it was possible until it happened to me one day.
