Actually Oregon was getting high turnout decades before they switched to vote-by-mail. There was one study which showed that Oregon got increased turnout from vote-by-mail, but a more recent study was unable to replicate that. It showed that Oregon's increased turnout was due to a "novelty effect", but it has since disappeared (except for a very small effect in some small special elections).
Furthermore, Oregon's anti-fraud measures are inadequate (e.g., the handwriting analysis isn't done by fully trained people, and has never been subjected to third-party scrutiny). And the much-touted "ballot parties" -- where groups of friends get together and talk about the issues and then fill out and mail their ballots out together -- are a classic example of a violation of the secret ballot and peer pressure in voting. (And remember: this doesn't actually increase turnout.)
Vote-by-mail increases the risks, doesn't effect turnout, and removes the secret ballot. But at least it's cheaper, I guess?
I do agree that online voting increases the risks monumentally, though. Even the much-lauded Estonian system is fundamentally flawed.