The duration of that flat area of the curve is not infinite


it is limited by the actual off-gassable surface area of your tank.
CO2 gas exits the water at a fixed speed, defined by it's
Henry's law constant. The volume of gas that is able to exit per unit time is strictly a function of your available surface area.
A clean air-water interface from a skimmer maximizes the rate of exit from that surface area, and agitation physically increases that surface area as well as disrupts the surface tension of the water. But the surface capacity is finite.
If you overdose, that concentration of injected CO2 will will overwhelm your available surface off-gassing capacity per unit time, and reach toxic levels in the water.