Well it does save money as well as space and weight. And if you're a purist.... [sm=72_72.gif]
I have a semi-autostart. That is a starter motor mounted on my engine but I connect to external gas for starting. I spin the starter and monitor the gas manually and the rest is automatic. It's easy and I really can't see any reason for full autostart.
As for the reliability/cooldown question... I have some 100+ hours on my engine. Replaced the bearings once because they had been damaged in a crash. No issues with overheating.
I haven't done any testing but I bet that we are way too concerned with this issue anyway. I bet that the fuselage will suffer more damage from a hot engine after shutdown than the bearings (mine's exposed

).