No. VRAM is important, but 12GB would be more than enough for a $150 graphics card, and there's not much point in getting extra VRAM when your GPU isn't powerful enough to use it effectively. 8GB is going obsolete, but it's still very rare to need more than that at 1080p (there are some games that use more, and they are becoming more common, but they won't be the majority for at least a couple of generations). It's not worth the cost of putting 16GB on a GPU that costs less than about $250, except for specialised workstation tasks; the overwhelming majority of people would be better off with a more powerful GPU with 12GB.
This will change in the future, as VRAM becomes cheaper and games become more demanding, but 16GB on entry-level GPUs will be a waste of money until 4GB GDDR7 chips (so you can get 16GB on a 128-bit bus without clamshelling) become available, which probably won't be until 2027 at the earliest.