I don't think - at least with current technology - that you can completely eliminate the "gets people sick" problem. The latency between head/eye/hand movement and the HMD's screen will eventually be eliminated, but you are still left with the problem of your brain. Your eyes ca be fooled to think that they are moving through the game's environment, but your brain has other inputs that tell it that your body is not moving or experiencing any acceleration/deceleration. That dissonance between inputs is what causes discomfort and nausea.
You can decrease these effects, by improving the experience and the immersion as much as possible. A good example is VR treadmills like the Virtuix Omni. It's more natural for your brain to experience a first-person shooter environment with the body in an upright position and walking, instead of sitting on a chair or couch while your eyes "think" you are walking.
Even with these improvements though, some people's brains might still be too sensitive to these differences from the real world. In the FPS example, even with a Virtuix Omni and a very good HMD, you still have other issues. For instance, there is no actual acceleration or deceleration when you walk/run/stop and your brain can tell. Even your character's height might throw your brain off, as it sees the ground in a different distance than what it's been used to for years.
Maybe in the future we'll see VR systems that tap into our brain and fool it on other levels, not just optical. Or who knows, maybe we're just not used to it yet and future generations, with VR available at birth, might adapt and overcome those issues.