This feature should not be implemented because:
It focuses on the original author of the question, which is often the wrong perspective.
It's not about the author. It's a little bit about them, but answers are for the whole community. The expectation is that others will be benefited by answers. As Wesley Murch says, even questions that have been resolved for the author may get more answers for the benefit of others.
It will often simply not work, for a variety of reasons.
The author may view the answer from another device, or another browser, or the same browser without being logged in. Many users first use a Stack Exchange site without registering, and their identity is stored in browser cookies. If they clear their cookies or use a different browser, they often are no longer logged in, and don't even know it. (This is why we have so many different user accounts with the same automatically generated avatar posting answers that should instead be edits or comments.) So, if implemented, this feature would not work right. A significant percentage of the time, it would not work at all.
When the OP sees the answer for a split second (or perhaps only partially loads the page, or loads the page fully but never sees the contents of that tab), then moves on because they didn't intend to return to their question yet, this feature would tell answer authors that their answer had been seen. That would be wrong.
When the OP goes to their question page deliberately but doesn't yet read a particular answer, this feature would wrongly tell answer authors that their answer had been seen.
It would violate users' privacy.
I think the idea this feature request hinges on is that, in part, a question and answer represent an exchange between the OP and the answer author. And that is true--that is one of the things a question and its answer are.
So, how would you like me to know when you've read a message I've sent you? An email, say? I can't answer for you, but I can tell you that if you had the ability to know when I opened email from you, I would consider that a violation of my privacy.
In fact there are technologies available to try to alert the sender of an email of when the email has been opened. They don't work very well, for a variety of reasons including analogues of some of the above reasons. Usually, an email contains an image with a long, recipient-specific serial number, hosted on an Internet server, and when the image is loaded (if you allow external images to load automatically in your email), the sender is notified.
And this existing technology is creepy. Anyone who uses it is creepy. This technology is one of the reasons I and many other people disable external images in our email, and many webmail providers disable automatically displaying external images by default.
Some answers are spam.
It would be bad for spammers to know when I've seen their spam answer to my question.
One of the reasons this is bad is that knowing how long it takes people to see their posts is critically important information for spammers to optimize their spamming techniques to reach more people. This is not the only source of information about that, but other sources of information about that (e.g., time to first downvote or to deletion) also serve positive anti-spam purposes.
Another reason we don't want spammers seeing this information is qualitative and subjective, and relates to the above issue of privacy. Do you really want spammers and other posters of abusive answers to know when you are reading their answer?
This is not as serious a problem as most of the other points here, but to overcome it there would have to be major advantages associated with this feature. Since whether or not the OP has seen the existing answers is not actually a very important factor in deciding anything, even this objection by itself is probably enough reason not to implement this feature.
It would erode the private nature of voting.
Suppose the OP sees my answer, and I get an upvote or a downvote at the same time. Was it necessarily the OP who voted? No, not necessarily. But:
Most likely they did. As the author of an answer to their question, I should not see this information.
Even if they didn't, many of the negative consequences of eroding voting privacy still apply. I may assume the OP upvoted or downvoted my question. If I'm a mean, abusive user, I may attack the OP for downvoting my question. These are all negative outcomes.
The OP can tell me what they want me to know.
The OP may choose to tell me they've seen my answer, tell me their reactions to it, tell me if they voted on it and how. This is their choice--it should not be taken from them.