Learning the “casual” form of verbs well will help you speak formally too.
There are many grammatical structures which require the use of the “casual” (i.e. standard) form. With that in mind you can’t just skip learning it because you’ll only be speaking/writing formally.
For example:
Suppose you want to say “where is (it)?” in Japanese politely. You’d say “どこですか？”
If you want to say “I don’t know”, politely, you’d say “知りません”. So far so good.
But what if you want to say “I don’t know where it is” politely? If you only know the polite forms, you would probably guess it is “どこですか、知りません”.
Unfortunately that’d be wrong. You see, the polite enders 〜ます and 〜です go at the end of the sentence, or row of sentences, (with a few optional exceptions) and they make the entire sentence polite. The rest of the verbs do not have to, and often must not, be in their polite form.
The correct way to say “I don’t know where it is” in polite Japanese is “どこだか、知りません”. This sentence is polite because the final verb has 〜ます attached to it.
The “だ” in there is not “casual” or “impolite”; it’s part of that grammatical structure.
Same goes for all sorts of verbs, not just the capula だ/です.
Polite vs Casual is mostly determined by the final verb:
| Polite (ます／です) | English | Casual |
|---|---|---|
| 彼は食べたか 知りません。 | I don’t know if he ate. | 彼は食べたか 知らない |
| 勉強するのが 難しいです。 | Studying is hard | 勉強するのが難しい。 |
| 歌うのが できません。 | I can’t sing | 歌うのが できない |
Notice how the polite sentences include “casual” verbs. 
The final verb/adjective with ます／です is what makes the entire sentence polite. The rest has to be “impolite”.
Conclusion
Do you understand now the reason why you can’t just skip learning the standard form of verbs, just because your classes require you to speak/write politely?
It’s not as easy as you think to “just learn it later” if you learn everything wrong from the start.