Responses
Having different sets for PvP & PvE skills is not unheard of, the mmorpgs I play (which also happens to be korean and another japanese) have this system. Specific PvP gear tend to be more of a Korean thing, I see it more in their mmorpgs. And if you have different set of skills, it would also make sense that having specific set of gear will also boost those specific attributes.
And it does take a lot of your time to grind for gear/ becoming good at the different skills (especially if you play both PvP & PvE for different classes ╥﹏╥)

from some korean webtoon i read about mmorpg, it seems they have a different set skill for normal gaming (aka farming) and PvP. skill that can be used in PvP cant be used in normal mode and vice versa. a different webtoon also mentioned the equipment used is also different. so it is possible one good at PvP wont be good at the other setting.
idk whether this is true for real life mmorpg in korea at least. but honestly this setting feel redundant. what do you mean they have to farm, enhance, and burn money for two different sets of equipment?? and they also have to build and learn to use two type of different skill sets for one character??
it is so different from mmorpg i usually found in japanese fiction. they usually have special area where PvP can be initiated but i havent seen one mention the different skill set or armor. they just use their normal skill set as it. it more cost and time effective.