Clearly when a TRV closes, the balance of the system is affected. However, since at a minimum all the radiators should receive sufficient flow when all the TRVs are open, then they should still receive sufficient flow when one or more TRVs close. So overall things continue to work. The actual adjustment of the TRV just changes the temperature at which it switches off. Well below that temperature, the radiator is operating as fully as the balancing intended, then it gradually closes over a few degrees until it is essentially turned completely off when the temperature is well above the level you set.
As more and more TRVs close, the total flow of water through the radiators drops until you just have water rushing through the one radiator that doesn't have a TRV, or through the bypass. The water flowing through the system will hardly drop in temperature and the boiler will barely have to run to keep it warm. Simple constant power pumps will be blasting the water through as hard as they can. None of this is ideal, but also not fatal and not something you can do a huge amount about. It is a compromise between doing what is ideal for the boiler vs doing what is ideal for your comfort and wallet, and the boiler loses with TRVs.
Some pumps incorporate constant pressure or proportional pressure controls to reduce the head as the flow rate drops, instead of pushing harder. Pretty much all boilers now can modulate down to reduce the heat output as the radiators turn off and are no longer shedding heat, although clearly they can never modulate down sufficiently to match the output of one small radiator. Careful siting of the main thermostat will help to avoid long periods with the boiler pumping hot water through almost nothing.