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For starters, Ohio does not have registration by political party. People will identify themselves as Democrats or Republicans but most voters in Ohio are independents.”

The first part is misleading and I don't know about the stats for the second. Although you don't register by party, your party affiliation is declared when you request one party's ballot in a primary. If you are neither you will get an issues only ballot in that primary. If you just blow off the primary every year and only vote in the general election you will be an independent by default. There used to be (and may still be) a requirement that if you wanted to change your party affiliation you had to sign an affidavit that you really did vote for your new party, but there is no way to check that and it is almost impossible to challenge it unless an election judge has personal knowledge that you are lying, like if you are a Democratic party official voting as a Republican to spoil a primary choice.