I would think that retzuos cannot touch the ground since they are tashmishei kedusha. But I see nearly everyone not being careful about this. The only source I can find that mentions the issue is the Kaf HaChaim who says it is no problem. Please clarify.
From what I have seen it seems that you are correct in your thinking. People are careful the tzitzis should not drag of be on the floor, and tefillin straps are more kadosh then the tzitzis strings, therefore one should be careful that they should not be on the floor.
Ginzei Hakodesh 6-12 in the name of the Shela Hakadosh (Kitzur Hashela- Miseches Chullin- HIlchos Tefillin, and Mekor Chaim (of the Chavas Yair) 25-11, Piskei Teshuvos 40-2 and ftnt. 17. I haven’t seen the Kaf Hachaim.