100 milliseconds is still an atrocious amount of latency in many contexts (typing for example). There were some Microsoft usability studies of tablets, people dragging their fingers on the touchscreen to draw things. They needed on the order of single-digit millisecond latency to make it feel immediate, because otherwise you could see the drawn brushstroke noticeably lagging your finger.
It's true that human reaction time is at roughly the 100ms timescale, but that got thoughtlessly transmuted into "latency below 100ms doesn't matter" (or 200ms or whatever they read), which doesn't follow at all. The hand-eye-brain system is a very complex prediction-feedback system, used to working in real life where there's usually zero real latency between what your fingers do and how the world reacts. When primitive man threw a spear, its ballistic trajectory started the instant it lost contact with his hand, not 100ms later.
Your brain is already doing the biological equivalent of lag compensation and rollback to account for how long nerve signals take to travel and how long muscles take to move and how fast its own neurons can process information. What you consciously perceive is a gestalt model, continuously smeared over what the brain thought the world was 100ms ago, and what it predicts it will be 100ms in the future. Adding more latency and jitter on top of that can only make the error rate worse.
And doubly so when there are different amounts of latency for the different sense modalities, e.g. visual vs audio vs tactile. I remember reading about a prototype for a sinister riot control weapon that echoed people's voices back to them at a slight delay, it totally fucked up the auditory feedback that underlies the ability to speak fluently.
See: https://danluu.com/keyboard-latency/#appendix-counter-argume...