Hi, Catherine! There are a couple of main reasons why pub owners only want drafts. A simple one is that Medium shows stories chronologically in terms of publishing. So depending on how busy the pub is (how many stories are added daily - or even hourly - and depending on when you publish, your piece might not even show up on the pub because it'll be too far down and no one will scroll that far.
The bigger reason is that submissions need to be in alignment with the pub's requirements. They're also representing the publication.
So pub owners and editors want to have a chance to check for typos and other issues. Is the content relevant? Does it need clarifying? Is there something that could be improved upon, which helps not only the pubs in terms of reputation for quality work but also helps writers get more reads, more followers, and it can increase the chances of getting Boosted.
Errors of grammar, punctuation etc. can be corrected. Incorrect formatting or capitalisation for title (and NOT capitalising the subtitle except for the first letter of the sentence) and all sorts of little things go into making a piece look its best. Not all editors bother; I don't change much, e.g. the issues people have with not knowing when to use numerals and when to write out the words, or what should be capitalised or how to not write in massive long blocks of text (ouch, so daunting to read!) - and other issues.
I'm super busy (as are most people) and I don't have time to change all of those things. I'll usually tidy the glaring errors (especially when I know English isn't a person's first language) but it bothers me when people are sloppy and submit pieces that seriously need more proofreading for typos.
As for being seen by a wider audience, yes, once a publication accepts your piece, that happens. But pub owners don't want to accept it until it fits their requirements. Hence - drafts only, please, as many will tell you!
Would love to have you at HHH, too, thanks for being willing to take a peek. Here's the link to the guidelines for you to have a look and see if it fits for you.
https://medium.com/hope-healing-and-humour/submission-guidelines-b0b0fa789490