Doing our own review of anything you write is a very good idea and should be done at various stages depending on the type of document you are creating. But it's important to remember that it's very difficult to find your own mistakes, which is why having a fresh set of eyes is so important.
Just like that commercial that talks about being "nose blind" to smells you're around all the time, the same thing happens when you're working closely on any written material - you become so familiar with it that it's hard to spot your own mistakes.
I've had a number of clients send me material that has been reviewed and approved as "final" and once I reviewed it, I was able to spot additional mistakes or typos that had been missed in prior reviews.
The other issue that people run into is relying too heavily on spell check and/or sites like Grammerly. These technologies are awesome, but they don't replace the need to perform a close review of any material, manuals, presentations or virtually any written content from being reviewed by someone with a strong grasp of grammar and spelling, and an eye for detail.