The reason students cannot write is they do not read. I didn’t say they can’t read; it’s that they DON’T read. You have to be a good reader before you can become a decent writer.
Which came first, the chicken or the can’t read. I can make a case that they can’t read so they don’t read. It shows up in their abysmal lack of vocabulary.
I once saw an editorial in the Houston Chronicle where the editor used “loose” when she meant “lose”. I see it all the time (in FR too) and it grates on me, but it isn’t the only confused use of English vocabulary that has become endemic in the population. The use of shorthand words and phrases in ‘texting’ will accelerate the decline in writing skills. Believe me, I’m not rotflmao.
However, your assertion that you have to have good reading skills—and use them—in order to become a decent writer is correct.