Intercoolers remove heat from the charge air (post turbo, pre throttle body). Intercooling makes no difference in turbo temperature.I think cooling down the turbo was something needed before they were all intercooled, something like the old Chrysler turbo I 2.2. Not a thing with modern turbos.
If I was running it really hard I'd probably let it idle for 30 sec or so before shutting it down, but completely unnecessary for normal driving.
In the early days of turbocharged cars, in the early 80s, for example, the turbocharges were often cooled by oil only.
Water-cooled turbos are not as susceptible to heat damage and coking as oil-cooled turbos.
So, now that they are all water-cooled, cooling down the turbo makes less of a difference.