They already give rendering priority to S ranks so we know it is possible. It would be interesting to hear why SE is not willing to do it with A ranks.
It's not influenced solely by what system you use to play the game. Plenty of PS4 users, even those without SSDs, report no issues during hunts.
The speed of your internet connection also plays a role. I know a few people who haven't changed their system but did upgrade to a higher speed connection in recent months and they've told me it has made a considerable difference in rendering at hunts.
You're going to have problems if you're at 250 kps while others are at 3 mps or better regardless of what system you're using. The game is shooting a lot more data at you when you're in a group of 100 players all in combat that when you're in a 4 man dungeons or standing around in Limsa.
A better system will also help, of course, but getting a better connection might be a simpler solution for some players.