Unedited histories are very chaotic and often contains errors, commits with partial features, abandoned code, reverted code, out-of-sequence code, etc. These are useful in preserving the actual progress of your own thought. But such histories are a nightmare to review. Commits should be complete (a single commit contains a full feature) and in proper order. If you're a reviewer, you also wouldn't want to waste time reviewing someone else's mistakes, experiments, reverted code, etc. Self-complete commits also have another advantage - users can choose to omit an entire feature by omitting a commit.

Now the part about having both - the unedited and carefully crafted history. Rebasing doesn't erase the original branch. You can preserve it by creating a new branch. Or, you can recover it from reflog. I use it to preserve the original development history. Then I submit the edited/crafted history/branch upstream.