I think there's gap of technical information here between old and new turbos.
Before Audi brought back their turbo, it's true many had bad experiences with them for the reason you mention - lack of cooling off.
Audi started using the turbocharged 1.8T motor since '95/'96 in the German market. This setup is different in that it has a coolant jacket around the turbo bearing. Coolant is circulated through the jacket by means of an electric pump. After shut-off, the pump works for a few minutes to cool down the bearing and prevent oil from coking. A properly maintained 1.8T should not have its turbo go out every 4-5 years. Always use synthetic oil and changed every 5k or if you're like me and have your oil analyzed, extend the interval to 7.5k to 10k miles.
My 1.8T (bought new in '01) currently has 205xxx on the original turbo. It's been chipped with APR 1bar since 50k.
The 2.0T motor is set-up the same way.