Need is relative, depends on your playstyle.
Will you still benefit from FCR6? Absolutely. That is how I run it but I have seen other posts where people are perfectly happy with no fc/fcr on protection mages for pvm. I have never tried it though.
I did a little searching in this forum, it seems that the general consensus is people still use FCR6 even in protection. Some actually add in the FC2 if they are going stone form because stone form will drop FC to -2 even in protection. Here is one such
link.
Went through that other thread. The last reply seems to indicate using the protection spell caps FC at 0. I thought it dropped your potential cap by 2. mage, mystic=0, necro=1, chiv, weaving=2 as capped under protection, is that wrong? going looking now.
*edit* okay so it looks like protection penalizes you by 2 FC but will not drop FC below zero, which I don't think I was aware of. Also UO Guide lists the max cast speed of Necromancers as the same as mages, which would be 2/6, but I could have sworn I remembered Necro being a wonky spell set with a casting time unto itself, 3/6. Playguide for skills is down and I can find nothing to substantiate either side.
In that case, if I am wrong, max FC for mages mystics and necros would be zero and unaffected by FC on jewels unless you are also using stone form, in which case FC2 would be required to prevent you from falling into a negative FC time.
Weavers and paladins in protection could still have a max FC of 2, but would have to be wearing 4FC to be at that cap.