Hardware unboxed texted Doom in 4k with two texture settings, ultra nightmare (~9GB of VRAM) and ultra settings (~7GB of VRAM).
A change in the texture settings did not affect the results of the GPUs that had enough VRAM to handle the highest texture settings (1080ti, Radeon VII, 3080 and 2080ti).
Every GPU that didn't have sufficient VRAM gained performance by reducing the VRAM usage.
Numbers from Hardware unboxed 3080 Review
Only setting changed was texture quality.
I have only selected a handful of cards to get a general picture, would you like me to do all of them?
The 980ti and 1070 were the only cards that didn't gain a sufficient boost in Avg frame rates (6% and 4% respectively). The 980ti only had 6GB of memory so even with Ultra textures it still didn't have enough VRAM, however there was an increase in performance (even if it was a small amount). I wonder how the results would have differed if the different texture settings were tested at 1440p or 1080p instead.
From hardware unboxed numbers it can be concluded that a change in texture quality for Doom has no impact on the frame rate of the game (see 1080ti, Radeon VII, 3080 and 2080ti results). It would be fair to conclude that other games will follow the same trend were texture settings would have no, or a small impact to frame rate.
Exceeding the VRAM buffer of these cards by 1GB, caused a significant decrease in framerates.
Reducing the VRAM, so that the GPUs did not exceed their 8GB of VRAM, caused average frame rates to increase by 20%-29% and minimum framerate to increase by 23%-40%.
For the 2080 super and non super, 2070 super and 5700XT, they ran out of VRAM before they ran out of GPU horsepower.