The pressure doesn't go away when the compressor isn't running, it just equalizes between the two side of the system. I don't think that the system knows the difference between the compressor not running because the engine is stopped or the compressor not running because it's declutched. Could be wrong, my says I frequently am.
From the above webpage:
"Thanks for your question about your Nissan Sentra. When your AC compressor isn’t running, the pressure in your system equalizes between the high and low side. What that pressure should be depends on the design of your system and the temperature outside when you take the measurement, but 100 psi with the compressor off may be just fine. When the compressor turns on it should lower the pressure on the low side of your system and that pressure again is dependant on ambient temperature and other factors. If the pressure isn’t lowering in your system with the AC switched on, then either your compressor isn’t running, or it has an internal failure.
Thanks again for your question!
-BD Auto Pro"
And this Toyota dealer has this about it.
From Top Gear, the explanation for turning it off has to do with electrical load when starting which once upon time made sense when starting a car was a bit of adventure as opposed to today's starts where the engine hardly spins before it fires.. But these days, I wonder if the cars aren't smart enough to disable the air conditioning system during cranking?