We definitely should not delete answers for being incorrect.
One of the main advantages of Stack Exchange over other parts of the internet is that we don't censor. Anyone can advocate whatever view they want as long as they do so respectfully. If we delete answers for being incorrect it can very easily lead to the censorship of certain viewpoints. While it doesn't happen very often, I've seen enough complaints about censorship already (i.e. even without deleting incorrect answers). Such complaints would only increase if we started deleting answers.
Additionally, how do we determine that something is objectively incorrect? You say it's objectively incorrect when it contradicts the Shulchan Aruch. I say it's not. You might say that a specific answer contradicts the Shulchan Aruch; I might say it doesn't. You might say that the Shulchan Aruch says XYZ; I might say that it doesn't. How do we resolve such disputes? No users inherently have more authority than others. Moderators are not specifically experts in the subject matter (though of course they often might be). High reputation also doesn't necessarily mean you have any authority. Perhaps you write very well, or perhaps you have a fanclub of upvoters.
The point is that for the most part there is no such thing as objectively incorrect. We have no way to measure this, and we have no way to adjudicate it or implement it. Remember that an answer only requires three votes to be deleted. Do we really want any three users with delete privileges to be able to decide that an answer is incorrect? Or a moderator to unilaterally decide that an answer is incorrect?
As I wrote in this post, deletion should be reserved for answers that do not address the question. In such a case we are not censoring any viewpoints, or arbitrarily deciding the correctness of any answers. We are only enforcing a policy of questions and answers rather than discussions.
Is it possible that incorrect answers will be posted? Certainly. But we have enough disclaimers about relying on things posted here that anyone who thinks that an answer is correct simply because it exists or has upvotes has no one to blame but themselves.
The above would be fitting for any Stack Exchange site. But all the more so for a site like this where we all know that there are many different factions, approaches, and methodologies within Judaism. For instance a kabbalah-based answer might be considered absolute truth by one user and absolute heresy by another user. The same holds true for rationalist answers, and various other categories as well.
If there is an answer which appears incorrect you can downvote, comment, and leave a better answer.