Why English is important: It actually depends on what you're using it for. For instance, on this website I use conversational English, which is often grammatically incorrect, in order to get my point across as efficiently as possible. But if you're writing a fiction novel, the way in which you write it is just as important as the plot. J.R.R. Tolkien and Roger Zelazny provide good examples of this. Other pieces online provide bad examples of writing, and fanfic is infamous for its poor construction. Copypasta pieces are often intentionally bad as well as hilarious. However, things like academic writing, resumes, business memos, research papers, and textbook writing all require you to understand how English is supposed to be strung together. Otherwise, no one will be able to focus on what you're trying to say. Errors in these things are distractions at best and misleading at worst and you don't want that.
If you are a doctor or otherwise need to have good handwriting, please do the rest of us a favor and practice. There's not really a way I know of becoming better at handwriting besides practice.
Big Brain Time