Your writing is not going to improve this way. You need at least one competent person editing and reviewing your writing. However, the idea/experiment is interesting and I may try it one day!
I disagree slightly. That's like saying you can't become a better cook without someone else eating and judging your cooking.
If you read a lot you have developed "taste" for good writing. When you're starting out, just writing something you yourself don't hate can be challenging (if you're honest with yourself). Heck, I re-wrote this comment 3 times before I didn't hate it :-)
I agree that eventually, once you're at a certain level, you need someone reviewing your writing.
The problem with this approach is that it's hard to measure progress. I can't objectively tell if my writing has improved (if I knew I was making mistakes, I wouldn't be making them). Popularity of a blog is also not a good metric because it depends a lot on how effectively you promote it.
There is obviously nothing wrong in leisure after work but the alternative can often be better. It can make you more skilled and more successful. It's an investment that reaps awesome benefits in the longer run.