I *believe* the fpr solenoid is actually used to ease hot re-starts and enhance hot re-start driveability.
In areas that use winter/summer blend fuels, there can be problems during the changeover time as the boffins mess with the reed vapor pressure of the fuel.
Matching rvp to the prevailing weather conditions is one of the things that makes a fuel more suited for extreme cold (or hot) operations.
Low outside temperatures means a high rvp fuel just won't want to atomize well on a cold start in a -20* morning. It wants to stay in droplet form and it won't atomise for sh*t.
Back when the world ran on carburetors, this was a big deal.
When they blend a fuel for winter use, they lower the rvp (and fiddle with a few other factors) to make it so it evaporates/atomises easily at low temperatures.
Using a winter blend fuel in hotter temps means it will boil off/percolate in the injectors/rail, leading to all kinds of hiccups on a restart as the vapors don't meter like liquid fuel.
Opening the the fpr solenoid on a hot restart will reference the fpr to ambient barometric pressure, (instead of manifold vaccuum) which will raise the fuel pressure.
This helps smooth out hot restarts, especially during the spring blend changeover and at high altitudes/high ambient temperatures.
Many folks do eliminate the fpr solenoid/attendent vaccuum lines for a cleaner engine bay.
If you live in gentler climes/lower altitudes, you might not even notice any effects from eliminating the fpr solenoid/system
Howsomever every now and then you'll see a thread from one of those folks that lives in area like colorado that has wild temp swings between summer and winter saying "why does my car run like sh*t after I let it sit for ten minutes at the store?"
... ymmv ...