Your game could end up using more VRAM than Crysis, and that's not a joke. 3D games are very efficient with textures - they can recycle the same textures over and over and over, and due to 3D models, lighting, shaders etc. they can keep it looking interesting. One tilable wood texture could be used on a log cabin, a forest of trees, a floor somewhere, a handle, tables, chairs, and so on.
Contrast that to a game composed entirely out of unique 1024x1024 textures, where there's no texture re-use. Your game is effectively a single, gigantic texture, which graphics cards don't tend to have enough memory for. On a card with 64mb VRAM, which you should support for integrated or older graphics hardware, you can fit sixteen 1024x1024 textures in memory (one is 4mb). And that's assuming it was empty to begin with, and it's not.
I'm not sure Crysis supports such low-end cards, but in theory a 3D game could just switch to ultra-low-res-crappy mode, using 256x256 textures for the 3D models. Then they can fit in 256 textures, which is probably enough for a small level. Note you can fit thousands of vertices of a 3D model in 1mb, enough for a lot of world or several models, so 3D stuff gets away with that much easier. Will you have a low-resolution version? Graphics cards don't have much memory since 3D games don't need it, so designing your game with such a lot of texturing is probably a bad idea.