I honestly don't see what logical argument can be made for this idea. The idea that the game will be better if they constantly have to try to appeal to two opposing sets of design philosophies while only allowed to make changes that blanket over everything is ridiculous.
Character progression. There wouldn't be many people willing to give up all their prestige items (mounts, achievements, gear) to play on a server with nothing but max level, geared, pvp characters.
I can't speak for everyone, but I wouldn't want to have to pay extra money for a separate server on top of a subscription fee for a pure arena experience. Not to mention buying the game and all of the expansions. Especially when you get a better pvp experience in other games without the ludicrous costs.
That being said, a server like that would be more competitive with everyone on a level playing field, and your voice is just as important as anyone's so keep fighting the good fight.
Character progression can exist on a pvp based relam. There are achievements and cosmetic upgrades that people would be very willing to progress towards. If things like glaives and shadowmourne were offered as cosmetic rewards for very high arena ratings or for X many wins then i'm sure that people would have no problem finding it rewarding to have a pvp only realm. Other cosmetic rewards can constantly continue to be added to make sure that progression is always something that can happen.
As for cost, there doesn't really need to be one. The current subscription fee is becoming out of date and that can be seen in other games that have shown enormous success without it (LoL is a great example). When I mentioned a year round tournament realm i just wanted to give some sort of reference that people would know about. I suppose a more accurate description would be that of Arena-Tournament.
For those who don't know, Arena-Tournament is a private server that is in a WOTLK patch. Unlike most private servers it does not have any PVE mobs and players are instantly presented with near max gear. Essentially it's a free, year round WOTLK tournament realm and it is vastly popular among a lot of pvpers that quit back in the day. Does the lack of progression make people not play? No. There are things like shadowmourne and glaives that have had stat reduction but still provide a good visual to work towards. This server is by far the most competitive version of WoW that i have ever seen. The only true drawback is that it doesn't often have patches so most of the balance/design issues that were apparent is season 8 are still there.
Arena-Tournament has a great pvp player base and things like BG afking simply don't exist. People actually have a reason to play BGs not to get gear, but because they are fun. This is what WoW should be learning from. These kinds of realms would be HUGE for the pvp community and would show a great increase in willingness to play pvp.