No one should be able to take an action on behalf of a user, be that a simple upvote, downvote, or acceptance. While there are automatic protocols to protect against suspect voting patterns, those are not intended to counter legitimate voting behavior, including the lack of voting.
While answer acceptance is the desired outcome, it is not the only means we have of identifying and rewarding good, useful, and correct answers. The acceptance checkmark is but one piece, and only the original asker can use it, but the rest of us can provide our input with our votes. Without the checkmark, our votes still accurately identify a viable solution, even if the user does not mark it is the solution.
Indeed, in your own examples, one answer has six upvotes, the other is the only answer and is also upvoted. The system is working, checkmark or not. Let it be.