Whether there is anything 'inelegant' about if and when is a matter of taste. Those who dislike it probably do so because it reminds them of the overly pedantic way of writing that is typical of legal documents. But the remedy for that is simple: if what is one is writing is not a legal document, one can simply use either if or when; one usually doesn't need both.
When logically implies if. If somebody instructs me 'When you see Phil, tell him I said "hi"' that means that I should wait until I see Phil, and then act accordingly. If I never see Phil, the occasion will not arise for telling him that. By following the instruction 'When you see Phil . . .' I will at the same time be following the possible instruction 'If you see Phil . . .'; it is thus not necessary to make the latter explicit. Of course, as a matter of pragmatics, when is likely to be used only if there is an expectation that I will actually see Phil.
If doesn't logically imply when, but, as has already been suggested in the comments, in most real-life contexts, it is likely to be treated as if it did. Suppose that somebody tells me 'If you see Phil, tell him I said "hi"'. When should I tell him you said 'hi'? The literal meaning does not say anything about the timing, but clearly I should not do that before I see him, because at that point I cannot be sure that I will see him. Moreover how would I go about telling him that before seeing him? It is also difficult to see how and why I would tell him that some time after seeing him. So obviously the only reasonable time to do it is when I see him. If thus for most ends and purposes includes when in such contexts, even though it does not logically imply it.
It is only when a great deal is at stake, and one wants to eliminate the slightest possibility that one's words will be misinterpreted, that one needs to resort to if and when, and that is typically the case in legal documents.
Of course there are plenty of other ways of saying the same thing, such as 'Your seeing Phil is a sufficient condition of your telling him I said "hi"' or 'Your seeing Phil will trigger your obligation to tell him I said "hi"' but none of them is likely to be particularly succinct or elegant.