All bluegrass seeding

Hi, I live in Zone 5, northern Illinois. Is it a good idea to seed all of my lawn with Bluegrass seed in early Sept. This way I will get a uniform, good loking lawn, Also, I am seeding in fall so, I am not worried about germination, let it take its time. Erosion may not be a problem as rain may not be as heavy as in spring. Thanking you in advance.
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