Your reference for [1] just states that bypassing the turbine is a thing, not that it's normally used.
First, reactors are in a stable equilibrium when operating, so one will actually increase their power by increasing the rate at which heat is removed (and v.v.). Alas, that's workable only within some small range.
A reason[1] load-following with PWRs was originally difficult is that traditionally PWRs use boron concentration in primary loop to regulate power and that can be decreased only slowly. The reason it's done that way is that it's the easiest way to ensure that power is adjusted uniformly throughout the core; if instead some control rods were partially inserted, the top part of the core would operate at lower power (and thus lower fuel burn-up) than the bottom part, which would cause compounding control issues later on.
France is using their PWRs in load-following mode by (a) having additional less absorptive control rods ("gray rods") that can be inserted fully to adjust power by smaller increments (b) more complicated schemes to decide which combination of available actuations to use to change power. See https://hal.science/hal-01496376/document for a paper that tries to optimize control designs so that power changes are more possible (and describes how the control schemes work).
Note that the total heat capacity of even just the primary loop in usual reactors is quite large: in PWRs it usually requires ~0.5s of full power output of the reactor to warm it by 1degC, so this can easily cover, say, ~5% variations for something like a minute.
[1] Another is that reactors are not stateless due to xenon poisoning.