To human perception a 0.1 seconds isn’t much different than 0.03 seconds

You are making the mistake of thinking about reaction times. What matters much more in shooters is that our brain adjusts for the ping. That affects:

• aiming with a lead of a few pixels. And in a fast moving environment, with skilled players, aiming for a lead of 30ms is absolutely a few pixels that can be targeted intentionally
• the time between triggering a shot (nerve signal to the trigger finger) and the last chance that the target has to dodge / change direction -> in such games, players are rarely running in a straight line, and more often running preemptive zigzag / evasive maneuvers even when not getting shot at. 30ms more ping means that on every shot taken, you lose 30ms from the window in which your target still moves in the direction you thought it was moving. Even if the target only changes direction only once per second, that's 3% lost from the time window in which you can predict where to shoot. Actually more, because you have reaction time after a direction change, before you can even consider aiming.
• furthermore, when a player with low ping gets hit by non-instant-kill ammo, they will dodge within their reaction time. Assuming the attacker chain-fires, they lose 30ms of ammo missing the target before they can adjust aim or stop firing