Explicitly declaring things like that in your language actually goes a long way towards making the language more rigorous and less dependent upon non-transliterated things along with all of the benefits of that (such as less likely to be misunderstood, etc.). Japanese actually does this a lot, for their stuff. For example in spoken English the way that you determine a question is all based around the speakers tone of voice, which leads to cases where if a person is deadpan enough it can be difficult to tell if they are making a statement or asking a question. On the other hand Japanese has particles (か "ka" and も "mo") that explicitly designate something as a question, removing that ambiguity. In the same way the honorifics work to eliminate ambiguity in the way people are talking, or the relative positions of a transliterated conversation. If you read one of the characters speak to another with a specific honorific, then you know for certain the relative positions of the two in the work (or at least what that particular one of them thinks the relative positions are), information that you would otherwise need to assume and guess at without them.
Personally in subbed works I don't find it that big of an issue, because you can literally here the character using the honorific. In dubs and and written works I tend to align much with RedKing. Drop them if there is a good English equivalent such as "professor" or something similar. However there are plenty of times where there isn't a good English equivalent, and I'd much rather have them there then have some bit of English press-ganged into serving to connotate something that it was never really meant to (I've seen more than one show that falls back on using a nickname in place of stuff and ends up with some really weird sections due to lost connotations). In short, don't use 'em if you can get away with it, but consider the entire context of what you are replacing and if necessary, leave them in.