Or you could "Keep Calm and File > Make a copy..." of the Google Doc and share that instead of the original draft. The copy doesn't copy the version history.
This is personal experience, so I'm not trying to be intentionally glib. Maybe for one person. For distributing to two to five people, this is a terrible idea, because here's how Mr. Murphy rolls: As soon as you get edits from A, B, and C of the team back, and update the document and are ready to distribute another version, the last person Y will submit their content. Person Y's content edits something that Person B already edited. This kind of thing snowballs...hard. It's not about them seeing the past, it's about appropriate control for the future (aka the deadline).
I mean, I know how to really whip the donkey spit out of "Compare" and the available tools, but until you've seen just how sideways this stuff can go, there's always room for a professional pest...an expert Proposal Writer...there's so much learned in the trenches that we all have a certain cynicism built up, and that's the fuel that gets the junk in by deadline time.
Honestly the only way I've found to make this stuff work is to use something like LaTeX, where the source is a text-based format, and then put it in a real version control system like git, that has proper support for merging and resolving conflicts. Then when the document is correct you compile it to a PDF, and that's what you actually send out (bonus: much smaller file size than something like word).
(Of course, the big downside is that all your collaborators have to know LaTeX, and not use funny macros that the others don't understand)
