Under what circumstances would you want to avoid LP mode, and when might it be acceptable?
Actually, I would have asked the question a bit differently. "Under what circumstances would I ever consider using LP mode?" The only answer that I can think of would be in a case where you absolutely could not change a tape. To answer your question, avoid LP mode if there is any motion, whatsoever, either camera, or subject. The savings in tape are not worth the quality hit, unless you are only going to output to tiny frame sizes, and using heavily compressed CODEC's where the quality will be poor, at best, to begin with. Good tapes are very cheap. You will appreciate the difference in the quality, by using them in SP mode.
Also, find a tape brand that you like and always stick to that brand and type. Many people recommend Sony, because the tapes are very slightly abrasive. Their feeling is that the tapes "clean" the heads, as they pass them. Some others choose other tape brands, because they are LESS abrasive, and feel that the wear on the heads more than offsets the cleaning aspect. One could do a lot of reading of reviews on tape brands.