I think, at a basic level, while it won't solve the problem, some good marketing would help.

Currently, a lot of people actually don't even know you get twice the reward for a first place VS a third. A lot of the people are just there for their daily, a static amount before match rewards, which is true, but I think if they knew they could get way more, they would try.

I also think the achievements are bad psychology. Inherently, there is nothing wrong with the mounts that require 100 wins. You can crassly rationalize it as 300 matches. It's actually realistically less due to capability as a player increasing and thus match influence increasing VS newer players losing more often, but I disgress. On the other hand, if it was, say second places count, and first places count for 2 wins., but the goal post was 250 or whatever, ultimately people would feel better. Look at how we even word first place as a "win", but we count second places a "loss". Just celebrating second places more would help a lot.

Unfortunately, in a game like FFXIV where you usually always win in all other environments, PvP does a good job of reminding people that in life, there are a whole lot of losers, and that's reality. PvP especially highlights competition, and competition highlights the haves and have-nots. I think pity rewards in PvP overall lead to a healthier environment than the detriment of people abusing the system... That said some more moderation to punish this behaviour would be ideal.