I don't really think that deleting your answers because no-one has reacted to them is the greatest use of your time, to be honest. There's little cost to the site to keep your answers available, and someone may come around later to whom they are helpful and who will provide you with some sort of feedback. And it does take some amount of your effort to periodically go through your "ignored" answers to decide whether of not to cull them. (I'll just add that not too long ago I had an answer accepted that was nearly three years old at the time. So it's never a lost cause.)
From the moderator side of things, you are to a fair extent free to decide what to do with your posts. If you do delete a fairly large number of them at a go, an automatic "potential vandalism" flag is raised for the moderators. While we're generally more concerned with users self-deleting (answered) questions, we'll take a look to see if anything has been deleted that is useful, and perhaps send a warning about not deleting too much stuff. Of importance, note that according to the Terms of Service
You grant Stack Exchange the perpetual and irrevocable right and license to use, copy, cache, publish, display, distribute, modify, create derivative works and store such Subscriber Content and to allow others to do so in any medium now known or hereinafter developed ... in order to provide the Services, even if such Subscriber Content has been contributed and subsequently removed by You.
While IANAL, in practice this seems to be taken to mean that even though you may choose to delete your posts, the "community" can decide to undelete them without seeking your explicit permission first. (Actually, you've already given permission.)
If you really care about getting some sort of feedback from askers when you provide an answer, one option is to be more picky about the questions you answer. This may include:
checking to see is the account of the asker is registered. Unregistered accounts have a tendency to get lost (by, say, clearing the cookies from the browser being used), and so these users are much less likely to return. You can check if a user is registered by going to their profile. If you do not see
the account is registered.
checking whether the user has responded to answers given in previous questions.
- if the user has sufficient privilege, check to see if they have ever voted. (The number of votes cast appears at the bottom of their profile.)
- check how much effort the asker put into the question. Greater care put into asking the question is very likely correlated to the chances that they will respond to your answer in some way.
Taking such factors into account, you can then decide whether you want to provide an answer. (This may/will result in a dramatic decrease in the rate at which you post answers.)
The other option, as mentioned by Bill Dubuque in a comment, is to learn to live with this situation: some of your answers will never elicit any response whatsoever.