You arent going to get much change here on the standard PS4. The PS4 PRO however will likely handle the crowded areas better due to its slightly higher clocked CPU. The PS4 runs the game really well actually. The only time you do see the frames drop down to what feels like around 15-20fps is in areas like idyllshire. In dungeons, raids, and open world areas the PS4 generally plays the game really well considering its hardware limitations, and majority of places keeps the framerate north of 40FPS. It should be noted that it does this while not sacrificing much with regards to Image Quality either. The game runs incredibly well on ps4, and really is one of the jewels on the ps4 for a online game.

The reason you see the ps4 frame rate dive in crowded areas is due to a CPU bottleneck. This is why you see little or no change when dropping from 1080p to 720p from the game settings. The reduction in resolution mostly just helps the GPU, and in these crowded areas the GPU isnt maxed out even at 1080p, because its essentially waiting on the CPU. So, while adjusting the resolution takes a load off the GPU, its still waiting on CPU.

The PS4 base model runs a multi core cpu that is only clocked at 1.6ghz. This is the root cause of the lag you see in idyllshire. The only way to alleviate this would be to scale the crowding down substantially, where you were only seeing maybe 1/4 of the people actually there. This would affect density and draw distance as well though in every area. FFXIV is tuned to the ps4 about as well as they can do it to keep the game playable in crowded areas without butchering its graphics quality in areas it runs just fine. The PS4 PRO will without a doubt handle ffxiv better in these areas. The PS4 Pro has the same CPU architecture as the base PS4 but is clocked at 2.1ghz instead of 1.6ghz. The memory is also sped up a little in the Pro. The biggest horsepower jump in the PS4 Pro comes to its GPU,which will more than double its theoretical performance. What will help ffxiv the most however is the bump in CPU clock. Its hard to say how many frames you will pick up with a 500mhz upclock, but it could put the framerate back to around 30fps in these areas, which would alleviate the noticeable jerky/laggyness you feel when running aorund and turn the camera in these crowded areas.

tldr; buy a ps4 pro if you want to see improvements without having to leave the ps4 platform.