Why increase pressure to go from liquid to steam? Assume the following phase diagram $T-H$ of water

At a nuclear engineering course, I was told that in order to increase the performance of a pressurized water reactor, one has to increase the pressure.
How such a reactor works is seen on the next image

In the steam generator the is saturated water. As fusion takes place, very hot water moves towards the steam generator where it transfers its thermal energy to the saturated water. The saturated water becomes hotter and finally it vaporizes. The steam moves the turbine and electric energy is produced.
I cannot understand the following: Why the increment of pressure in the reactor vessel, will transfer more energy in the steam generator making the thermal energy of the steam larger?
 A: Its simple - with more pressure, you've got more particles to carry the energy per $m^3$. Liquid is better carrier of temperature than gas, because it has better Thermal conductivity and with pressure, you can prevent the water becoming steam.
That is the difference between inner and outer circle on your image. The outer circle on the other side, profits from big difference in pressure.
A: I'm not a nuclear engineer, or a power systems engineer but lets try to work the question as simply as possible.


*

*You want the maximum efficiency out of the turbine.

*That is a large fraction of the thermodynamic (Carnot) limit which is set by the temperature of steam entering the turbine and the design of the turbine. The only parameter you can change dynamically here is the temperature of the input steam (and you want it to be as hot as possible).

*The steam can be no hotter than the water leaving the core of the reactor, and will actually be a bit less because of latent heat.

*Assuming that you want to maintain the core-cooling loop liquid the whole way (I believe that you do), the only way to raise its temperature is to increase it's pressure (because this increases the boiling point, which is your upper limit).


So, to maintain high power generation efficiency you must maintain high pressure on the core cooling system.

You need to keep in mind that there are two separate loops at work here. One is in contact with the core and potentially contaminated, so it is kept carefully inside the containment vessel. The other one is nominally clean and actually powers the turbine. You can see this in the figure you posted: one is colored in oranges, yellows and reds; the other colored in shades of blue (and actually a third water system that provides the cold sink for the back of the turbine also colored blue, but it plays only a passive roll here).
Steam is generated in the clean loop by exchanging heat with the hot liquid water in the dirty loop. Latent heat only comes into play on the clean side. I don't know if that system is actively pressurized or not, but there will be some back pressure in the system from the turbine.
