Flexible Antenna Systems (FAS) are a key enabler of next-generation wireless networks, allowing the antenna aperture to be dynamically reconfigured to adapt to channel conditions and service requirements. In this context, pinching-antenna systems (PASs) implemented on software-controllable dielectric waveguides provide the ability to reconfigure both channel characteristics and path loss by selectively exciting discrete radiation points. Existing works, however, typically assume continuously adjustable pinching positions, neglecting the spatial discreteness imposed by practical implementations. This paper develops a closed-form analytical framework for the ergodic rate of two-state PASs, where pinching antennas are fixed and only their activation states are controlled. To quantify the impact of spatial discretization, pinching discretization efficiency is introduced, characterizing the performance gap relative to the ideal continuous case. Finally, numerical results show that near-continuous performance can be achieved with a limited number of pinching points, providing design insights for scalable PASs.