I am very wary of turning in essays on a blog, simply because there is so much plagiarism going around. It would both put hundreds of essays out there, for students to copy, and for students to submit via copy/paste. Granted, it's not difficult to plagiarize on paper, but with paper, there is no option to "delete entry." The evidence is there, turned in by the hands of the students.
I've actually caught more cases of plagiarism since going paperless. Every now and then, I take classtime with my students to run Google checks on anonymous blogged essays their peers have turned in. Inevitably, we find copied work. Rather than bust students and deal with it in the standard disciplinary way in the event we do discover fault, I use it as a means to show them how easy it is to discover plagiarism in the digital world. The kids learn quick and I've never had to do this more than once with any class to completely discourage digital copying. It's actually quite a bit more difficult to do that with just paper.
And as for the concern over "delete entry"... let's just say that few things you ever write online actually disappear. And if it's a blog, and you've subscribed to it, you actually get sent a copy directly to your inbox or newsreader. The writer can't take it away from you.
With paper, there are no accusations that the teacher may have manipulated the essay, through a word processing program.
Most blogging apps leave a time-stamp and author signature on the post. Consider that one safe-guard to any accusations. It's got the student's name on it and it's got the exact time and date that they posted it. Just refuse to accept any work that's not posted with a time-stamp.