No, the OP should not be able to prevent further answers.
The primary purpose of a Stack Exchange site is to build an excellent documentation resource in question-answer form. (See the about page for any Stack Exchange site; for example, the one for Stack Overflow. "With your help, we're working together to build a library of detailed answers to every question about programming.") Even if the OP is right to think future answers won't help them--and it would be difficult to really know this!--they may help others.
Questions are about their authors. But they're more about the community at large, and they're even more about the documentation-creating project that the community is collaborating on. For the same reason people besides the OP should be able to see questions and answers, so too should it be possible to add new answers.
Accepting an answer serves the purpose of indicating that it solved the OP's problem according to the OP. That's its sole purpose. Whether or not a question has an accepted answer doesn't say anything about whether or not further answers would be helpful.
Furthermore, additional answers even after an answer has been accepted frequently help the OP too. They may present alternative solutions, or better versions of solutions that have already been posted.