Single transistors in modern processes switch currents orders of magnitude lower than milliamps. More like micro- to picoamps. There's leakage to account for too as features get smaller and smaller due to tunneling and other effects, but still in aggregate the current per transistor is tiny.
Also the transistors are working at 1V or lower, but as you say they are FETs and don't have the same Vbe drop as a BJT.
Also the transistors are working at 1V or lower, but as you say they are FETs and don't have the same Vbe drop as a BJT.