Make the drop rate 1% or less- so low it's very much worth the time saved to buy it. The rise of smartphone games nickle and diming people to death with purchasable productivity/ability to even PLAY the game after you run out of stamina is proof of that. If you give someone the choice of waiting to get lucky or paying "reasonable" fee to get what they want, a depressing amount of people will simply pay up.
Farming savage mounts can be extremely tedious, but you still need to have the requisite skill to farm the encounter. Something mindless like story dungeons are not indicative of player skill unless said players are somehow not able to breathe, move forward, and press some buttons at the same time. Adding optional tedious grind for a minuscule chance of getting lucky doing something that even the most brain-dead players are supposed to be able to complete will not diminish the worth of Savage/EX mounts. And the option to buy it and skip the chore of running the instance will be very appealing to the kinds of people who already buy mounts and stuff from the shop. For the rest of us, it's something we can try to gamble for. You can still have your mount when you want it and everyone else can still safely ignore it or run old, necessary content repeatedly to try for a drop.
No one needs anything in the cash shop to play and enjoy XIV. But to me it's stark naked greed on SE's part to have cash-shop only items when we pay a sub to fund the game's entire existence in the first place. I'm not saying they shouldn't try to make more money, but they could at least take the sting out of seeing a $20 mount for sale by giving us SOME way of trying to earn it, even if the odds are stacked against us.
Heck, I've been playing since 2014 and have nothing to show for my loyalty except for thousands of achievement points I can't use. Why not convert them to a store credit of some kind? Maybe not enough to pay for the mount entirely, but enough to bring it down to a price I'd settle for since SE is indirectly rewarding me for playing the game and supporting them for all these years. I'd be ok with buying a mount or emote or some such thing if I could somehow credit all of my in-game effort towards the price in some way.