And continue to be exploited. You left out that piece.
Really? I thought I had that covered by "have long been exploited, and that genie is not going back in the bottle."
My question back is, "Why is secrecy more important than accuracy?"
Because the harm done by vote-forcing and vote-buying far outweighs the harm done by all but the most egregiously inaccurate counts. It takes little more than a cursory glance at modern societies facing these problems to see that.
For a stable society, no "other party" cares enough to force people to vote a particular way. It just doesn't happen...
At best, that assumption is extremely naive. Even in places that practice secret ballots, attempts at vote-selling and coercive schemes are common. In places with a free press, they make the news all the time.
They don't tend to get very far, of course. But that's largely because it's impossible to verify that any given person actually voted in a particular way. There is no point in attempting to coerce someone to do something when all you have to verify that they've done what you wanted. There is no sense in buying votes when there is no way to verify that you've actually gotten the service you paid for. But for this to work, there must well and truly be no way to get that information.
Legal and procedural safeguards are not enough. It must be actually impossible to get this information: in other words, the secret ballot. There is a tradeoff involved, in that counts become marginally less accurate, but given the alternative, this price is worth paying.