It would be nice to have the option, though realistically, it won't really make a difference performance-wise.
All this setting really changes is the maximum amount of VRAM that can be allocated for the texture streaming pool.
Increasing the max amount of the streaming pool won't really make it use up more in minimum conditions.
I've just tested with it set to the max setting of 8GB of VRAM, and on Kings Canyon it's mostly using up 3.3GB of VRAM.
Assuming I would encounter a lot of other users & particles, I could see it going up to 6, though even hitting 8 would seem like quite the task.
Currently (From what I've seen), Apex uses a lot of textures that usually are around 1024x1024, but some textures are 2048x2048.
I cannot really see how those textures are used, but with textures around those resolutions, I don't think they would be hitting the cap of 8GB anytime soon.
Unless they decide to make higher quality textures (Which I believe would be unlikely due to the game focusing mostly on it's competitiveness), it would seem unecessarry to increase it.
You could change the texture streaming budget manually, but I cannot confirm if this actually works since the game never really takes up that memory to begin with.
Inside of this folder: %userprofile%\Saved Games\Respawn\Apex\local you will find the videoconfig.txt that contains most of your video settings.
Inside of this file, you can find the texture streaming budget under this setting: "setting.stream_memory"
I have not been able to find out how these values exactly correspond to the amount of VRAM that's being taken up, though this is what I did find out:
2gb = 160000
2-3gb = 300000
3gb = 600000
4gb = 1000000
6gb = 2000000
8gb = 3000000